Even though your father was born at home, he should have been registered.
Check first with your family to make certain they do not have a copy of it. You did not indicate where your father was born, but just google the place that he was born to see how to obtain a birth certificate. You will have to fill out papers to get it, and pay a fee. It all depends on where he was born, etc. Once you get it, than you can work with the information that was given.