There's another consideration. No two batteries are exactly the same. When connected in parallel, the one with lower internal resistance will discharge the other one. So, even with no use they will deteriorate faster than if not connected together. My opinion, and personal usage, is to use them separately, monitor voltage, and swap the batteries when one shows first sign of discharge. I look for about 11v on a 12v system, under mild load of a few amps, then swap.
Second advantage of using them separately is that different types, models, even chemistry, batteries can be used. One goes bad, just replace one. One of my house batteries on the camper is a 110 AH deep discharge. The other is a 75AH marine type, not true deep discharge. I have even used wet cell nicad (36AH) as the second battery.
As for charging, they can certainly be charged from the same source at the same time. If that source is solar, even better, as solar power is a current source rather than voltage source. Add a small 'spreader' resistor in series (just half an Ohm works well), diode isolate them, and connect them to the solar charger permanently (and independently from your load switching). BTW, I don't use a charge controller at all. My battery capacity is so high compared to solar panel output (couple of amps) that there is no possible way the solar panels can over charge the batteries between camping trips (a couple times a month minimum). Simple is better.
The camper house batteries also recharge off the truck system when we're on the road (charged through a 24 to 12v converter set to 13.8v).
Bob