You would have the inverter run off the house batteries but have the alternator charge the house batteries as you travel. This assumes that you have a 12 volt coach electrical system. If you have a 24 volt alternator, it can be done by using a Vanner equalizer. You need a big alternator though. My 24 volt, 45 amp alternator is only good enough for normal vehicle functions. In my case, I could mount a 12 volt alternator on the engine separately to charge the house batteries, but it will not be the monster needed to run AC. People like me run the generator if we need AC while traveling.