One thing to consider with an inveter/charger is that the ones I have seen, including my OUTSTANDING Outback 3232(!!!), do not have multiple battery bank charging capability. So if you want to retain the dual, electrically separate battery banks, you would have to buy an additional charger. If you wish to combine the batt banks, which is actually more efficient for power and battery life, then it's not an issue. However, doing so would eliminate the safety factor of having a separate house and start bank. So it should be carefully considered before doing so.
There MAY be some inverter/chargers that can support charging of separate/isolated banks, I just haven't seen them. ALSO, if you have a 12v or 24v system, you could use the inverter/charger and a battery isolater to maintain the separate banks. If you have a 32v system, there are no 32v isolaters made - again, at least that I could find after much searching.