Jenkins is also servlet and servlet filter based. If you check the "Enabling security" and "allow container to authenticate" checkboxes in jenkins configuration, jenkins displays in the page header the username authenticated by httpd.
Its filters are able to understand both basic and digest authentication headers received from httpd proxy.
But Jenkins does not seem to provide any
inbuilt env variable to get the username. Perhaps
this plugin may do the trick, but I didn't try it out.
Another problem with this approach is that you can't log out, because the Authorization header is sent by httpd proxy for every request, until browser is closed.
I'm not very familiar with Jenkins or its authentication, but I get the impression from its config page that Jenkins prefers to do its own authentication and authorization. Its source code shows it uses the very capable acegi security toolkit. I'm guessing that Jenkins authn and authz are much more refined than a simplistic in-or-out authentication from the apache proxy. Perhaps
you should consider doing the authentication on jenkins side rather than on httpd side, and then try that plugin.
I also get the impression that the authenticated user is not very important, because your question has been asked in multiple forums and has remained unanswered as far as I could find. Perhaps there is some other approach. Sorry I can't provide a better answer, since I'm not very familiar with Jenkins.