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So, you should be able to run both, just be careful that the extension matches the appropriate language.
<insert humorous tone of voice here>
We wouldn't want to needlessly make things more complicated, right? I mean, if you can, make sure to be simple, and simplify things, so that it doesn't take 10, or 20 words to do that which should only take 2, got it? good, now go forth and spread the good words.
</humorous tone>
A couple of things to bear in mind:
You can't pass session data between ASP and ASP.NET (Actually, you can but it's a massive pain).
As someone else mentioned, remember that ASP uses .ASP extensions, and ASP.NET uses .ASPX extensions, when you view pages in the browser.