diff -u b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
--- b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
+++ b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
@@ -56,7 +56,7 @@
    * @param \Drupal\Core\Extension\ProfileHandlerInterface $profile_handler
    *   (optional) The profile handler.
    */
-  public function __construct(StorageInterface $config_storage, $directory = self::CONFIG_INSTALL_DIRECTORY, $collection = StorageInterface::DEFAULT_COLLECTION, $include_profile = TRUE, $profile = NULL, ProfileHandlerInterface $profile_handler) {
+  public function __construct(StorageInterface $config_storage, $directory = self::CONFIG_INSTALL_DIRECTORY, $collection = StorageInterface::DEFAULT_COLLECTION, $include_profile = TRUE, $profile = NULL, ProfileHandlerInterface $profile_handler = NULL) {
     parent::__construct($directory, $collection, $profile_handler);
     $this->configStorage = $config_storage;
     $this->includeProfile = $include_profile;
diff -u b/core/lib/Drupal/Core/Extension/ProfileHandler.php b/core/lib/Drupal/Core/Extension/ProfileHandler.php
--- b/core/lib/Drupal/Core/Extension/ProfileHandler.php
+++ b/core/lib/Drupal/Core/Extension/ProfileHandler.php
@@ -71,7 +71,7 @@
   public function __construct($root, InfoParserInterface $info_parser, ExtensionDiscovery $extension_discovery = NULL) {
     $this->root = $root;
     $this->infoParser = $info_parser;
-    $this->extensionDiscovery = $extension_discovery ?: new ExtensionDiscovery($root);
+    $this->extensionDiscovery = $extension_discovery ?: new ExtensionDiscovery($root, TRUE, NULL, NULL, $this);
   }
 
   /**
@@ -91,12 +91,11 @@
     // @todo Remove as part of https://www.drupal.org/node/2186491.
     $modules_cache = &drupal_static('system_rebuild_module_data');
     if (!$this->scanCache && !isset($modules_cache)) {
-      $listing = $this->getExtensionDiscovery();
       // Find installation profiles. This needs to happen before performing a
       // module scan as the module scan requires knowing what the active profile
       // is.
       // @todo Remove as part of https://www.drupal.org/node/2186491.
-      $profiles = $listing->scan('profile');
+      $profiles = $this->extensionDiscovery->scan('profile');
       foreach ($profiles as $profile_name => $extension) {
         // Prime the drupal_get_filename() static cache with the profile info
         // file location so we can use drupal_get_path() on the active profile
@@ -126,7 +125,8 @@
         'php' => DRUPAL_MINIMUM_PHP,
         'base profile' => [
           'name' => '',
-          'excluded_dependencies' => []
+          'excluded_dependencies' => [],
+          'excluded_themes' => [],
         ],
       ];
 
@@ -139,6 +139,7 @@
         $info['base profile'] = [
           'name' => $info['base profile'],
           'excluded_dependencies' => [],
+          'excluded_themes' => [],
         ];
       }
 
@@ -154,6 +155,13 @@
         $info['dependencies'] = array_diff($info['dependencies'], $info['base profile']['excluded_dependencies']);
         // Ensure there's no circular dependency.
         $info['dependencies'] = array_diff($info['dependencies'], [$profile]);
+
+        // Ensure all themes are cleanly merged.
+        $info['themes'] = array_unique(array_merge($info['themes'], $base_info['themes']));
+        // Apply excluded themes.
+        $info['themes'] = array_diff($info['themes'], $info['base profile']['excluded_themes']);
+        // Ensure each theme is listed only once.
+        $info['themes'] = array_unique($info['themes']);
       }
       $profile_list[$profile] = $profile;
       $info['profile_list'] = $profile_list;
diff -u b/core/profiles/testing_inherited/testing_inherited.info.yml b/core/profiles/testing_inherited/testing_inherited.info.yml
--- b/core/profiles/testing_inherited/testing_inherited.info.yml
+++ b/core/profiles/testing_inherited/testing_inherited.info.yml
@@ -9,6 +9,12 @@
-  name: minimal
+  name: testing
   excluded_dependencies:
-    - dblog
+    - page_cache
+  excluded_themes:
+    - classy
 
 dependencies:
+  - block
   - config
+
+themes:
+  - stable
diff -u b/core/profiles/testing_inherited/tests/src/Functional/InheritedProfileTest.php b/core/profiles/testing_inherited/tests/src/Functional/InheritedProfileTest.php
--- b/core/profiles/testing_inherited/tests/src/Functional/InheritedProfileTest.php
+++ b/core/profiles/testing_inherited/tests/src/Functional/InheritedProfileTest.php
@@ -2,6 +2,8 @@
 
 namespace Drupal\Tests\testing_inherited\Functional;
 
+use Drupal\block\BlockInterface;
+use Drupal\block\Entity\Block;
 use Drupal\Tests\BrowserTestBase;
 
 /**
@@ -20,14 +22,19 @@
    * Tests inherited installation profile.
    */
   function testInheritedProfile() {
-    $this->drupalGet('');
-    // Check the login block is present.
-    $this->assertSession()->linkExists(t('Create new account'));
-    $this->assertSession()->statusCodeEquals(200);
+    // Check that the stable_login block exists.
+    $this->assertInstanceOf(BlockInterface::class, Block::load('stable_login'));
+
+    // Check that stable is the default theme.
+    $this->assertEquals('stable', $this->config('system.theme')->get('default'));
 
     // Check the excluded_dependencies flag on installation profiles.
     $this->assertTrue(\Drupal::moduleHandler()->moduleExists('config'));
-    $this->assertFalse(\Drupal::moduleHandler()->moduleExists('dblog'));
+    $this->assertFalse(\Drupal::moduleHandler()->moduleExists('page_cache'));
+
+    // Check that all themes were installed, except excluded ones.
+    $this->assertTrue(\Drupal::service('theme_handler')->themeExists('stable'));
+    $this->assertFalse(\Drupal::service('theme_handler')->themeExists('classy'));
   }
 
 }
only in patch2:
unchanged:
--- /dev/null
+++ b/core/profiles/testing_inherited/config/install/block.block.stable_login.yml
@@ -0,0 +1,19 @@
+langcode: en
+status: true
+dependencies:
+  module:
+    - user
+  theme:
+    - stable
+id: stable_login
+theme: stable
+region: sidebar_first
+weight: 0
+provider: null
+plugin: user_login_block
+settings:
+  id: user_login_block
+  label: 'User login'
+  provider: user
+  label_display: visible
+visibility: {  }
only in patch2:
unchanged:
--- /dev/null
+++ b/core/profiles/testing_inherited/config/install/system.theme.yml
@@ -0,0 +1,2 @@
+# @todo: Remove this file in https://www.drupal.org/node/2352949
+default: stable