The generator "should" charge the house batteries. BUT it does so indirectly by powering the CONverter which actually does the job, the same way it does it when plugged in to 120V. If plugging in does result in charging as desired, then wire chasing may be in order. A Battery under charge should read 13.5-14.5 Volts, the extra voltage boost coming from the charger itself. A fully charged battery alone should read about 12.6V or so.
The Chassis (starter) battery is probably not charged unless the engine is running but that can be remedied by adding a unit like the Trk-L-Start to maintain its charge while plugged in. Running the engine should also charge the house batteries.
Remember, charging batteries is not a 5 minute affair, it takes many hours to charge them properly.
Years, makes and models of the Class C, the converter and/or main power panel would really help in diagnosis.