A quit claim should only change title but will have nothing to do with the lien against the home for the mortgage.
Unless your friend is willing to make an offer to the bank and is capable of financing it in his name then I do not believe this option exist. Scott was correct in suggesting the deed in lieu of. Other options include Short sale, attempting a loan modification or finding out if the Help 4 Homeowners will work for you.
If you are in Orlando, I will be happy to discuss more private particulars to allow you a true look into your options. I am also a licensed mortgage broker with short sale negotiation experience. But all I can promise is an honest assessment and an honest opinion.
I hope we have answered your question.