The house battery(s) are supposed to be charged by a converter/charger device that gets power when your rig is connected to "shore"
AC power . The house battery(s) power the interior lights, appliance controls, furnace blower, etc. if your converter/charger is working and properly connected to your house battery, the house battery should read 13.6 volts at the battery terminals after charging for 24 hours. When your chassis engine is running, the alternator should be charging both your engine starting battery and your house battery if the solenoid device is working properly. If you have an RV generator installed and it is properly connected with a transfer switch or by plugging the shore cable into the generator receptacle, it supplies AC power to the converter charger which in turn charges the house battery. When you have the shore power cable connected to camp power, the converter charger charges the house battery BUT NOT engine starting battery . If you park the rig for a month, the starting battery may be dead from self-discharging and power drawn by alarms, radio memories, and other "parasitic" loads. The more you know about these 12 volt DC and 110 volt AC systems and how to operate, test and maintain them, the better they will serve you when needed. Owning an RV is a hobby in itself, a truck full of appliances and devices operated by 110 volt AC and 12 volt DC power and propane systems.