Hi There, I have a 2012, have had it since new and it definitely charges both. I believe that the Chassis battery is a trickle charge, Mine stays around 13.1V when I am plugged in. My House batteries sit around 13.4 when plugged in. I was just in mine today getting it ready for a trip.
Hope that helps
GR
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GrantR
Itasca Ellipse
Silverado Duramax Toad
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