Your biggest issue is state. In ASP, chances are you threw a lot of crap into the Session object. ASP.NET (MVC or web forms) and ASP do not share the same session (state), so you end up having to store state somewhere to have it continue to work.
As long as you can get a place to store the state that both ASP and ASP.NET MVC can both consult, you can start migrating the pages piecemeal. If you cannot figure that out, you will have to scrap the ASP after you completely rebuild the site in ASP.NET MVC.
NOTE: I have been leading migrations (ASP >> ASP.NET (both flavors) and VB >> VB.NET). Unless you absolutely have to use a mixed mode, you are better to rebuild and then migrate the site over rather than rely on a mixed site. The worst thing that can happen is somebody stored something stupid in session or application, that you did not envision, and you are now in a place where you are not keeping something important. And you probably find it after a user complains about some transaction they did that did not migrate and now you no longer have any information about it.
NOTE 2: Sometimes clients want to migrate piecemeal and refuse to listen to you stating it is a bad idea. Your option, at this time, is move on to another client (or job) or do it. If "do it" is the option, make sure you have your butt covered, as this is a minefield.