As many have replied, web sites aren't projects, so they don't build a DLL.
My solution to this problem is to never use a Web Site.
I'm kinda learning by trial and error, but I found (with VS 2005) that
Web Applications lacked some of the development features in VS that
Websites had. For example, the "ASP.NET Configuration" that brings up
the Website Administration tool for a website didn't seem to work
right (or wasn't even offered - I can't remember) when used with a Web
Application. And when I added code files to the App_Code directory of
a web application, I had a dickens of time getting them to be included
in the build. Setting "trace" in the web.config file didn't seem to
work consistently for a Web Application. A bunch of other little
things.
But it was a shocker when I loaded my Website to my hosting platform
and discovered that it was re-compiling everything on the fly,
sometimes with build errors that were not present when building under
VS. That's when somebody told me about "Publish Website", which DOES
do a build to .dll. So that's what I do now.