--- a/testing/mochitest/browser-test.js
+++ b/testing/mochitest/browser-test.js
@@ -725,19 +725,18 @@ Tester.prototype = {
         stack: err.stack,
         allowFailure: currentTest.allowFailure,
       } : {
         name: message,
         pass: true,
         stack,
         allowFailure: currentTest.allowFailure,
       }));
-    });
+    }, true);
 
-    this.PromiseTestUtils.Assert = this.currentTest.scope.Assert;
     this.ContentTask.setTestScope(currentScope);
 
     // Allow Assert.jsm methods to be tacked to the current scope.
     this.currentTest.scope.export_assertions = function() {
       for (let func in this.Assert) {
         this[func] = this.Assert[func].bind(this.Assert);
       }
     };

--- a/testing/modules/Assert.jsm
+++ b/testing/modules/Assert.jsm
@@ -20,25 +20,35 @@ Components.utils.import("resource://gre/
 Components.utils.import("resource://gre/modules/ObjectUtils.jsm");
 
 XPCOMUtils.defineLazyModuleGetter(this, "Promise",
                                   "resource://gre/modules/Promise.jsm");
 /**
  * 1. The assert module provides functions that throw AssertionError's when
  * particular conditions are not met.
  *
- * To use the module you'll need to instantiate it first, which allows consumers
+ * To use the module you may instantiate it first, which allows consumers
  * to override certain behavior on the newly obtained instance. For examples,
  * see the javadoc comments for the `report` member function.
+ *
+ * The isDefault argument is used by test suites to set reporterFunc as the
+ * default used by the global instance, which is called for example by other
+ * test-only modules. This is false when the reporter is set by content scripts,
+ * because they may still run in the parent process.
  */
-var Assert = this.Assert = function(reporterFunc) {
+var Assert = this.Assert = function(reporterFunc, isDefault) {
   if (reporterFunc)
     this.setReporter(reporterFunc);
+  if (isDefault)
+    Assert.setReporter(reporterFunc);
 };
 
+// This allows using the Assert object as an additional global instance.
+Object.setPrototypeOf(Assert, Assert.prototype);
+
 function instanceOf(object, type) {
   return Object.prototype.toString.call(object) == "[object " + type + "]";
 }
 
 function replacer(key, value) {
   if (value === undefined) {
     return "" + value;
   }

--- a/testing/xpcshell/head.js
+++ b/testing/xpcshell/head.js
@@ -46,17 +46,17 @@ Components.utils.importGlobalProperties(
 var AssertCls = Components.utils.import("resource://testing-common/Assert.jsm", null).Assert;
 // Pass a custom report function for xpcshell-test style reporting.
 var Assert = new AssertCls(function(err, message, stack) {
   if (err) {
     do_report_result(false, err.message, err.stack);
   } else {
     do_report_result(true, message, stack);
   }
-});
+}, true);
 
 var _add_params = function(params) {
   if (typeof _XPCSHELL_PROCESS != "undefined") {
     params.xpcshell_process = _XPCSHELL_PROCESS;
   }
 };
 
 var _dumpLog = function(raw_msg) {
@@ -505,17 +505,16 @@ function _execute_test() {
 
   _register_protocol_handlers();
 
   // Override idle service by default.
   // Call do_get_idle() to restore the factory and get the service.
   _fakeIdleService.activate();
 
   _PromiseTestUtils.init();
-  _PromiseTestUtils.Assert = Assert;
 
   let coverageCollector = null;
   if (typeof _JSCOV_DIR === "string") {
     let _CoverageCollector = Components.utils.import("resource://testing-common/CoverageUtils.jsm", {}).CoverageCollector;
     coverageCollector = new _CoverageCollector(_JSCOV_DIR);
   }
 
   // _HEAD_FILES is dynamically defined by <runxpcshelltests.py>.

--- a/toolkit/components/passwordmgr/test/LoginTestUtils.jsm
+++ b/toolkit/components/passwordmgr/test/LoginTestUtils.jsm
@@ -11,30 +11,24 @@ this.EXPORTED_SYMBOLS = [
   "LoginTestUtils",
 ];
 
 const { classes: Cc, interfaces: Ci, utils: Cu, results: Cr } = Components;
 
 Cu.import("resource://gre/modules/Services.jsm");
 Cu.import("resource://gre/modules/XPCOMUtils.jsm");
 
+Cu.import("resource://testing-common/Assert.jsm");
 Cu.import("resource://testing-common/TestUtils.jsm");
 
 const LoginInfo =
       Components.Constructor("@mozilla.org/login-manager/loginInfo;1",
                              "nsILoginInfo", "init");
 
-// For now, we need consumers to provide a reference to Assert.jsm.
-var Assert = null;
-
 this.LoginTestUtils = {
-  set Assert(assert) {
-    Assert = assert; // eslint-disable-line no-native-reassign
-  },
-
   /**
    * Forces the storage module to save all data, and the Login Manager service
    * to replace the storage module with a newly initialized instance.
    */
   async reloadData() {
     Services.obs.notifyObservers(null, "passwordmgr-storage-replace");
     await TestUtils.topicObserved("passwordmgr-storage-replace-complete");
   },

--- a/toolkit/components/passwordmgr/test/unit/head.js
+++ b/toolkit/components/passwordmgr/test/unit/head.js
@@ -7,33 +7,30 @@
 // Globals
 
 let { classes: Cc, interfaces: Ci, utils: Cu, results: Cr } = Components;
 
 Cu.import("resource://gre/modules/XPCOMUtils.jsm");
 Cu.import("resource://gre/modules/Services.jsm");
 Cu.import("resource://gre/modules/LoginRecipes.jsm");
 Cu.import("resource://gre/modules/LoginHelper.jsm");
+Cu.import("resource://testing-common/LoginTestUtils.jsm");
 Cu.import("resource://testing-common/MockDocument.jsm");
 
 XPCOMUtils.defineLazyModuleGetter(this, "DownloadPaths",
                                   "resource://gre/modules/DownloadPaths.jsm");
 XPCOMUtils.defineLazyModuleGetter(this, "FileUtils",
                                   "resource://gre/modules/FileUtils.jsm");
 XPCOMUtils.defineLazyModuleGetter(this, "OS",
                                   "resource://gre/modules/osfile.jsm");
 
 const LoginInfo =
       Components.Constructor("@mozilla.org/login-manager/loginInfo;1",
                              "nsILoginInfo", "init");
 
-// Import LoginTestUtils.jsm as LoginTestUtils.
-XPCOMUtils.defineLazyModuleGetter(this, "LoginTestUtils",
-                                  "resource://testing-common/LoginTestUtils.jsm");
-LoginTestUtils.Assert = Assert;
 const TestData = LoginTestUtils.testData;
 const newPropertyBag = LoginHelper.newPropertyBag;
 
 /**
  * All the tests are implemented with add_task, this starts them automatically.
  */
 function run_test()
 {

--- a/toolkit/modules/tests/modules/PromiseTestUtils.jsm
+++ b/toolkit/modules/tests/modules/PromiseTestUtils.jsm
@@ -1,35 +1,30 @@
 /* Any copyright is dedicated to the Public Domain.
  * http://creativecommons.org/publicdomain/zero/1.0/ */
 
 /*
  * Detects and reports unhandled rejections during test runs. Test harnesses
  * will fail tests in this case, unless the test whitelists itself.
  */
 
-// For this test we allow the global Assert to be modified.
-/* global Assert:true */
-
 "use strict";
 
 this.EXPORTED_SYMBOLS = [
   "PromiseTestUtils",
 ];
 
 const { classes: Cc, interfaces: Ci, utils: Cu, results: Cr } = Components;
 
 Cu.import("resource://gre/modules/Services.jsm", this);
+Cu.import("resource://testing-common/Assert.jsm", this);
 
 // Keep "JSMPromise" separate so "Promise" still refers to DOM Promises.
 let JSMPromise = Cu.import("resource://gre/modules/Promise.jsm", {}).Promise;
 
-// For now, we need test harnesses to provide a reference to Assert.jsm.
-let Assert = null;
-
 this.PromiseTestUtils = {
   /**
    * Array of objects containing the details of the Promise rejections that are
    * currently left uncaught. This includes DOM Promise and Promise.jsm. When
    * rejections in DOM Promises are consumed, they are removed from this list.
    *
    * The objects contain at least the following properties:
    * {
@@ -131,23 +126,16 @@ this.PromiseTestUtils = {
    * Called by tests that have been whitelisted, disables the observers in this
    * module. For new tests where uncaught rejections are expected, you should
    * use the more granular expectUncaughtRejection function instead.
    */
   thisTestLeaksUncaughtRejectionsAndShouldBeFixed() {
     this.uninit();
   },
 
-  /**
-   * Sets or updates the Assert object instance to be used for error reporting.
-   */
-  set Assert(assert) {
-    Assert = assert;
-  },
-
   // UncaughtRejectionObserver
   onLeftUncaught(promise) {
     let message = "(Unable to convert rejection reason to string.)";
     try {
       let reason = PromiseDebugging.getState(promise).reason;
       if (reason === this._ensureDOMPromiseRejectionsProcessedReason) {
         // Ignore the special promise for ensureDOMPromiseRejectionsProcessed.
         return;

--- a/uriloader/exthandler/tests/HandlerServiceTestUtils.jsm
+++ b/uriloader/exthandler/tests/HandlerServiceTestUtils.jsm
@@ -11,32 +11,26 @@ this.EXPORTED_SYMBOLS = [
   "HandlerServiceTestUtils",
 ];
 
 const { classes: Cc, interfaces: Ci, utils: Cu, results: Cr } = Components;
 
 Cu.import("resource://gre/modules/AppConstants.jsm");
 Cu.import("resource://gre/modules/Services.jsm");
 Cu.import("resource://gre/modules/XPCOMUtils.jsm");
+Cu.import("resource://testing-common/Assert.jsm");
 
 XPCOMUtils.defineLazyServiceGetter(this, "gExternalProtocolService",
                                    "@mozilla.org/uriloader/external-protocol-service;1",
                                    "nsIExternalProtocolService");
 XPCOMUtils.defineLazyServiceGetter(this, "gMIMEService",
                                    "@mozilla.org/mime;1",
                                    "nsIMIMEService");
 
-// For now, we need consumers to provide a reference to Assert.jsm.
-var Assert = null;
-
 this.HandlerServiceTestUtils = {
-  set Assert(assert) {
-    Assert = assert; // eslint-disable-line no-native-reassign
-  },
-
   /**
    * This has to be initialized to the nsIHandlerService instance under testing.
    *
    * When support for migration from the RDF to the JSON back-end is removed,
    * this can be replaced by a lazy getter for the default implementation.
    */
   handlerService: null,
 

--- a/uriloader/exthandler/tests/unit/head.js
+++ b/uriloader/exthandler/tests/unit/head.js
@@ -22,18 +22,16 @@ Cu.import("resource://testing-common/Tes
 
 XPCOMUtils.defineLazyServiceGetter(this, "gHandlerServiceJSON",
                                    "@mozilla.org/uriloader/handler-service;1",
                                    "nsIHandlerService");
 XPCOMUtils.defineLazyServiceGetter(this, "gHandlerServiceRDF",
                                    "@mozilla.org/uriloader/handler-service-rdf;1",
                                    "nsIHandlerService");
 
-HandlerServiceTestUtils.Assert = Assert;
-
 do_get_profile();
 
 let jsonPath = OS.Path.join(OS.Constants.Path.profileDir, "handlers.json");
 let rdfFile = FileUtils.getFile("ProfD", ["mimeTypes.rdf"]);
 
 /**
  * Unloads the nsIHandlerService data store, so the back-end file can be
  * accessed or modified, and the new data will be loaded at the next access.