Our first check was the Apache config, which appeared correct. Next was a web search where I found some links to the apache weblogic bridge. The bridge incorrectly places a text/html mimetype on everything. We fixed this by putting the mime mapping into the web.xml file of our webapp. Everything works beautifully again!
Here's the mapping that needs to be added:
<mime-mapping>
<extension>css</extension>
<mime-type>text/css</mime-type>
</mime-mapping>