First, let's make some assumptions clear.
The "ASP.NET MVC" is based upon a proven standard, known as the "Model-View-Controller" architectural pattern. This is not a new invention from some Microsoft geek; quite the opposite, this pattern has been used by several frameworks since 1979.
So, what is "the model"? Using a more modern term, it is the domain logic. It is your business entities, your data access objects, even some of your static declared enumerations and collections: anything that is used by your application, has business value and is not related to some specific presentation issue or requirement.
That's why I said your question, deep inside, does not make much sense.
After you tried to explain what your question is about, and after jim and Darin Dimitrov answers, I guess what you really need, what you are really asking about, became a little clearer: what you want to know is how to bind your existing, pre-MVC business layer with the C and the V of an ASP.NET MVC application.
So, if you do have a well designed BLL layer, and, more importantly, if your BLL and DAL communicate through some DTO's, you could, theoretically, bind them directly to your views.
If those DTO's need to be transformed in some way (because they could not be directly understood by the end user, for instance), this should be done by the use some "ViewModels", which are basically another set of presentation specific DTO's, plus data-annotations for server-side data validation. This transformation, of course, should be done by your controllers.
Some MS people will say that you MUST use viewmodels, and that if you don't use them you will rot in hell. I do not entirely agree. Of course, there are several advantages in using view models (like the already mentioned data-annotations, compile-time verification, intellisense and so forth), but if many other successful MVC frameworks are fine without them, I don't think it should be different with ASP.NET MVC.
That's my 2 cents.
Edit Another important advantage of using viewmodels is related to security: by exposing a set of presentation-only DTOs, the real domain-objects become somewhat protected.