Here is my reply to your other post, same subject.
I don't know specifically about your MH but usually when the MH is plugged in the coach (house) battery will be charged, the chassis battery will not.
When driving, both the coach battery and the chassis battery will be charged.
To check yours, measure the battery voltage when nothing is running and not plugged in, then when plugged in. If the battery voltage is higher when plugged in, it is being charged. You can check if being charged while the engine is running the same way.
