Is it permissible for my (non-Muslim) father to buy a house with an interest-based loan, on condition that I share my money with him, with the intention of living in it with my family?

It is impermissible to seek an interest-based loan. However, if a father obtains an interest-based loan and purchases a house with it, there is no objection to participating with him in its purchase, rental, renovation, or sale. "Partnership is valid even if disliked, such as a partnership with a dhimmi, an usurer, or one whose wealth is mostly unlawful."