Alex, you have two seperate but connected electrical systems. A 12 volt
system and a household 110 system.
As supplied from the factory it works like this: the furnace fan, interior lights, the water pump, and any exhaust fans run off 12 volts dc, supplied from the coach battery or batteries. You should also have a couple of 12 volt
power recepticals that look something like the socket for a cigarette lighter. There are 12 volt circuits for the running lights and electric brakes as well, but that is a seperate issue. There will be a fuse box with 12 volt fuses - someone else will have to tell you where, but it will be near the converter (more on it anon). Absent electric power input (shore power, solar cells, generator) you will be limited in the use of these items to the capacity of the battery.
In addition, you have a standard 110 volt ac circuit. It supplies the air conditioner, if you have one, the refrigerator, the 110 outlets for coffee pots, television sets, radios, or whatever you plug in, and the converter. The converter (or Univolt, in Airstreamspeak) is a transformer and battery charger that will recharge your coach batteries and run the aforementioned 12 volt items above. It is what you hear humming when plugged into shore power. There will be a disconnect/fuse box located on the inside of your coach somewhere near where the shore power cable enters the shell.
As supplied by the factory, that is all you have. There is no way to run 110 appliances, including the airconditioner, off the 12 volt battery. There is a device called an "inverter", however, that will change 12 volt dc into 110 ac. These are not a factory item. There are all sizes available, and can be (but usually are not) wired directly into the 12 volt supply to deliver 110 power to the household outlets in the coach. The problem is that you are limited to the watt-hour capacity of the batteries, and most 110 volt devices consume LOTS of watts - coffee pots, toasters, microwaves, hair dryers, etc. Modern tv's are not too bad, and are the most frequent use for an inverter. To run the air conditioner you need the battery pack they use to jump start the space shuttle.
I'm guessing you do NOT have an inverter. I am guessing you are mistaken in thinking you got 110 power out of the outlets without being conntected to shore power. I am guessing your system is functioning exactly as it should.