How can I parallel a battery supply and AC supply?
You cannot connect battery output with AC source. As mentioned captcha a battery produces DC (direct current) and it cannot be mixed with AC power supply.
The best solution for you it will be to connect two same batteries in parallel. It must have the same output voltage. Check this link for more information.
Also you can use a battery charger (credits to captcha), but it may require additional circuits to protect the AC/DC converter or battery and may a filter required.