Even though ASP.NET was written specifically for the Windows Platform there has been a really active movement in the Linux community to bring C# and the .NET framework over to their OS as well. This project is called Mono. From what I've read it is indeed possible to run ASP.NET with a C# code base on an Apache Linux based system.
Please realize that this is latest technology and literally hasn't been out yet for more than a couple months. You'll be exploring a new type of system setup. I has and can be done. In fact, I've just installed Fedora Core 2 in hopes of trying out the mono project and possibly ASP.NET in a linux environment as well.
Hope this answers your question. If not, I'll see what I can do, as will others on this board.