Easy question first: Does your domain mapping plugin work on sub-directory installs?
More advanced question: Can you map to a URL with a path or filename appended to it?
As an example:
So if I were to type "www.somesite.com/blog/index.php" into my browser I would see the contents of "www.mynetwork.com/somesite/" as a desired result.
This particular situation won't work if I get redirected back to "www.somesite.com" as their WWW traffic serves other content.