Disagree with prior responses, but yes you can.
Nigal,You can do what you want, but I disagree with something in each prior response. First, don't get a regular "car" battery. Diesels require a little bit more to get them going, so I would go for a marine that is used for diesels. Also, with only one house bank, it may come to use to back up your house on the rare occasion.Second, while the engine is running (charging) you may get by with mixing batteries, but the AC charger will not like it at all. The newer ones have settings for wet, gel, etc., and that controls the cutoff-at-full-charge voltage, as well as the "quick charge" amperage levels. You could cook one type to make the happy. Don't mix the types, go with all gel or all wet.If you are interested, I have a setup with two house banks using 4 six-volts and a 5th battery for a starter. it could be modified for 2 12-volt house and a single starter to give the same arrangement as you might be looking for. The advanage is that the house banks are always isolated, and everything is always charging without touching any of the battery selector switches. No "forgetting", and you still can switch for backing up a dead bank somewhere.Good luck,Steve