The house (coach) battery should be charged off the engine when the engine is running. There's some sort of an isolator system that connects them together when appropriate; often but not always it uses the same solenoid and wires as the emergency jump start button, activating them when the engine is running.
I had to replace that solenoid in my motorhome earlier this year, as a matter of fact. There are other things that could fail in the system, blown fuses or broken wires for instance. Occasionally I guess there are switches to manually control if the coach battery charges or not, but that's very much the exception rather than the rule these days. It's hard to think of very many circumstances where one would not want it to charge from the engine while underway.
