Is it permissible for me to partner with my father in buying or building a house, all of his money being unlawful in terms of its acquisition, for the purpose of living in it or renting it out?

There is no harm in you and your father buying a property jointly, with each of you paying his share and then independently owning his portion of the property. This is because the sanctity of wealth relates to the conscience of its acquirer and not to the essence of the wealth itself. Therefore, if wealth is acquired through a permissible means, then there is no objection to it.