i was quite a late 'convert' to mvc, after having been both a classic asp and webforms developer for over 10 years. however, about 18 months ago, a project came along that our management team decided would be a good self contained project to trial mvc on. I was tasked with managing the project. I'll admit that i was VERY sceptical as we had a large collaterol of components built for webforms as well as our own 'mini framework' for webforms projects.
imagine my surprise when I slowly found that being closer to the metal with the mvc paradigm was actually a more productive process. soon, i even began to question whether to go webforms or mvc on other new projects that were starting up. the beauty was that our webforms projects used the 3 layers approach that you mention and for us, it was quite easy to switch out the webforms portion and slot our BLL/DAL into place and use within the mvc project.
The long and the short of it is that it'll take time to get up to speed on the concepts of mvc but thankfully, there are many great books and tutorials out there:
http://nerddinner.codeplex.com/
http://blog.stevensanderson.com/
http://www.amazon.com/ASP-NET-Framework-Second-Experts-Voice/dp/1430228865/ref=pd_sim_b_2
i'd recommend the steven sanderson book, if it's the only one you ever look at. it ties together a very comprehensive walk thro on many core concepts, leading to a very detailed understanding of 'how it all works' by the end of the piece.
In short, no, designing with 3 layers doesn't = mvc. however, if you're worried about losing the knowledge and core functionality that you've built in your 3 layer approach, you needn't be. mvc and the BLL/DAL can work together just wonderfully. there is a fear when moving from webforms that you lose all the previous dpmain logic - in short, they happily merge/co-exist and it's entirely possible to still have part of the team working on the business logic whilst another part deals exclusively with the mvc implementation of that.
I was going to drone on about the excellent jquery integration - but that's a tale for another day :)