The two house batteries should be charged by the converter/charger while you are plugged into 120volt "shore power". The are also charged by your engine's alternator when you are driving. The engine starter battery is not charged by your converter/charger when rig is plugged into shore power. Your house batteries are also charged when you are running your RV generator but it takes hours of running the generator to recharge house batteries. Your rig probably has a auxiliary/house battery disconnect switch connected to a relay which disconnects and connects your house batteries. If disconnected, batteries will not charge from the converter/charger. When disconnected, batteries are not powering alarms, etc and will stay charged longer when rig is parked for long periods, not connected to shore power. If connected/switch on, house batteries should charge from the converter charger, if rig is connected to shore power and converter/charger is working properly, batteries and converter will power the interior lights and other items such as electronic controls in your appliances and alarms. When house batteries are down/discharged, it takes many hours for the a typical older converter charger to bring them back up, similar to a trickle charger. The engine alternator should recharge house batteries while you drive for a few hours/to your next destination. It is not good to run your batteries down, it will shorten useful life. Most RV house battery setups have marginal capacity, try to conserve house battery power when not connected to shore power.
Every RV owner needs to learn how their RV's battery charging systems work, wiring, fuses and circuit breakers, how to clean battery connections, how to check voltages with a simple multi-meter and how to check and maintain battery electrolyte levels. You might find that a modern converter charger will do a better job of charging your house batteries without overcharging and damaging them over time.
Progressive Dynamics Model 9245, converter is easy to install and not very expensive.