As others have said, there nearly always is some arrangement to charge the house (coach) battery from the engine alternator, with varying degrees of sophistication. The gizmo that accomplishes this is the battery isolator, of which there are a few different styles: some all-electronic/solid state ones that are basically just a high-current diode, or somewhat more commonly a high current relay that connects the two together along with some sort of control circuitry. At its simplest, this control circuitry may just be the ignition switch.
With the relay based isolators, usually the relay performs double duty as the switching element in an emergency start circuit.
There are various gizmos available (but less frequently installed by the factory) that charge the chassis battery from the converter output. One effective and fairly inexpensive one is the Ultra Trik-L-Start. (Some of the fancier battery isolators are set up to work bidirectionally when either battery is charging, too.)
On my motorhome, the dash lighter sockets connect to the chassis battery (and are switchefd with the ignition), and the steps connect to the house battery, but are only manually controlled. They only consume power when the rocker switch is pushed to extend or retract. These sorts of details vary a lot from maker to maker and sometimes from model to model.
