In general, I'm always in favor of keeping real estate in the family. Building dynastic wealth is much harder when everyone is sending money out of the family for various reasons.
In this case, however, I'm not sure I like your plan. You're proposing paying interest to a bank so that your parents can have extra income now. Wouldn't it be better to just have your parents do seller financing, and you pay them your mortgage payments directly?
Taking it a logical step further, they would then pay you rent to offset what you are paying them in mortgage. See how silly this is?
I think a better solution is to just have your parents leave you the house in their will. They would still get to live there as long as they like, and you would inherit the property with whatever residual mortgage they still have on it. Same net outcome, way less extraneous fees and expenses.