You won't overcharge the one while charging the other--the voltage of both batteries has to be the same when they're connected together in parallel (well, excepting differences due to wiring voltage drops in the interconnects). You'd see some current flow (particularly at the onset) from the charged battery bank into the discharged one as the voltages equalize.
Ideally I suspect the best approach would be to connect the discharged battery only to the solar charger until it is charged to about the same level of charge (voltage) as the charged (and presumably now discharging) house bank, and then connect them together. However, unless the discharged battery is quite large in comparison to the charged one, I can't foresee any great trouble with connecting them together from the start. Do use sufficiently heavy interconnect wire for safety.
