Best setup for a 12V house system is to have both the house and starter battery grounded. The house battery is connected on the + side to the vehicle battery via an isolator relay
that closes when the alternator charges. This way, the house battery gets charged from the alternator but house loads do not drain the starting battery when the engine is off. Every consumer, whether on house or starter battery, is grounded for the current return path.
A isolator diode can be used in lieu of the isolator relay but you need to compensate for the voltage loss in the diode with a separate sense lead to the alternator. That's a little trickier especially if the alternator is monitored/controlled by the ECU.