I have a website that I would like to add registration and plans (ex: premium membership, free membership) and charge the customers on a monthly subscription basis. The existing website is written in ASP.NET and I'd like to know if there's a framework that I can use to tie in the different plans and the payment provider.
There is no framework you can slap on that can handle this for you. So much of it is dependent on how your application is built, how the data is stored, etc. It sounds like yours is custom built as opposed to using software? If so, your best bet is to hire someone to integrate it into your software.
What do you use for account management? Does that software offer an option to add and manage products, like subscriptions? If yes, you're 75% ready to go. Before you go and buy any software, ask yourself a question -- will people pay for these features when the web is so saturated with all kind of freebies.