Index: wp-content/themes/twentythirteen/functions.php
===================================================================
--- wp-content/themes/twentythirteen/functions.php	(revision 23458)
+++ wp-content/themes/twentythirteen/functions.php	(working copy)
@@ -542,7 +542,7 @@
 	}
 	return $content;
 }
-add_filter( 'the_content', 'twentythirteen_aside_date', 0 ); // 0 to ensure before everything else.
+add_filter( 'the_content', 'twentythirteen_aside_date', 8 ); // After embeds, before everything else.
 
 /**
  * Add postMessage support for site title and description for the Customizer.