It's a great product where it takes into account what the value of your home will be AFTER the work has been completed. So in this case you would refinance what you owe, plus the costs to do the renovations, and that would be compared to what the value of your home would be after the work. Often times, you are creating equity that you did not have before.
Not every lender does these, and many do them poorly! My company has a deicated 203K division that makes borrowers(and other parties involved) very comfortable with the transaction and process. Please feel free to contact me for more info.
If you have further questions I am local 603-396-9176 please give me a call.
Since your parents are giving you the rest of the money, all should be good.
The best idea is to talk with a qualified mortgage broker.
If you need a name, email me email@example.com and I will send you a name of a person that is really good.