With the Website Template in Visual Studio, all classes in the App_Code directory of your web site is compiled into a temporary assembly of its own when the web app is loaded by IIS. In order to get a handle to the assembly, you can use the following code snippet:
Assembly a = Assembly.Load("__code");
Of course, in Mono it doesn't work that way. To get the temporary compiled assembly you need to use the following:
Assembly a = Assembly.Load("App_Code");
Note that like everything on Linux, the casing matters here! "app_code" will not work, unless you're running XSP on Windows.
Strangely enough the Mono implementation makes more sense. I couldn't find any information on the interwebs about this issue, so I eventually got it by guessing the correct name!