Good question. There is probably a relay that allows cross-connecting house and chassis batteries for emergency starting - maybe that relay is stuck in the closed position (it is normally open) or the switch for it has shorted and causing the relay to stay closed.
In newer rigs the house charging system may also charge the chassis battery, to keep it topped up while in shore power for extended periods. There is supposed to be isolation to prevent drawing power in the other direction, but maybe it has gone bad or was miswired?
There may also be an accessory installed that is effectively cross-connecting the two battery systems, i.e. it is wired to both the hose and chassis batteries. I've seen that done to make an accessory work "both ways", but it will cause problems like yours.
What's the condition of the house batteries?
Is your inverter an integrated inverter/charger like a Heart or Xantrex, or is it an add-on inverter only, with a separate converter/charger for charging. Each has different wiring and differing possibilities for this sort of problem.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL