Whose name is on the mortgage? It sounds like your husband is paying rent which happens to cover the mortgage. Since the parents own the home, I don't believe you have any claim to it or its equity.
If it's in their name, then he is not the one paying the mortgage directly. He may be paying them back (and that could even be by him dropping the payment directly to the bank) but if it's in his parents name, then their name is on the mortgage from a legal standpoint.