I have a 2002 Itasca Suncruiser. When connected to shore power or running the generator, only the coach batteries get charged. With the engine running, both coach and chassis batteries are charged. Newer coaches have corrected the deficiency, probably with a battery isolator, which charges two or more sets of battery banks , but as the name implies, keeps them isolated.
I also learned the hard way, and now use a trickle charger to keep my chassis battery charged (when parked).
There are some charger/converters or charger/inverters that have more than one dc output, and hence can charge two or more battery banks.
BTW, a lot of RVers use an AMP-L-START CHARGER exactly to solve the problem of charging the chassis battery. There is lots of discussion about this on the iRV2 forums.
John & Mary Ann
2002 Itasca Suncruiser, IFG32V
2013 Honda CRV