Running an AC with a battery is not that simple.If the voltage rating of the AC is 110V of course it will start with a 110v battery. but for running the AC,power is needed. Power is P=V*I in simple terms.(AC power is a bit more complicated actually). So this battery need to supply the current ( which will also be given by the manufacturer as specification) for as long as the AC runs at 110V. this current rating is high for AC.So u will need a very large battery to run this.

Please clarify your question.

Do you want 2 x 110 V ac supplies from the 110 V dc battery.

What are you trying to achieve? 

You will get better answers if we know what you are trying to do.