Allow HTML in Excerpts
By default, WordPress strips all HTML tags from excerpts. To allow them, simply replace the filter that creates the excerpt from your content.
First, copy the default excerpt filter from wp-includes/formatting.php:
By changing the strip_tags parameters, you can allow whatever tags you want:
Also be sure to change the name of the function. Copy this to your functions.php file.
Then, replace the default filter with your new one in functions.php: