Most lenders will have a six month "chain of title" that will require the property to be in your name for that period of time. You may be able to do the mortgage as a second home, instead of a refinance; however, that would necessitate you providing evidence that you will not be renting/subletting the property at any time. The advice given regarding your parents mortgage being due in full is true...all mortgages have a "due on sale/transfer" clause that basically calls the note due. Very few lenders will exercise this option as long as the mortgage payments are made timely. And, your new mortgage will be a refinance, not a purchase. ...the determining factor is whether your name is on title or not. If it is (as in your case), it is a refinance. If not, it would be a purchase. Best of luck.
@Pandabear: Your situation is completely different. The only way you can "have nothing to do with this home" is to have your parents refinance/purchase it from you. Same guidelines apply regarding names on title. However, the fact that you took out the mortgage means you are responsible for it and nothing can change that except a purchase or refinance. Simply quit claiming the property to your parents will do nothing to remedy your situation: You give away the house, but keep the debt. Best to you also.