Hi,
the pix is not a 'complete' router. When packets arrive at the inside interface, they can not be sent out on the same inside interface.
Isn't it possible for your internal clients to use the internal ip address of the web server? If that is possible and your dns servers are on the outside interface, you could use the alias command to do 'dns-doctoring'. More info about that on this URL:
http://www.cisco.com/warp/public/110/alias.html
Don't hesitate to post your questions.
Kind Regards,
Tom