Hi Jimnkarens,
The inverter associated with the Residential Refrigerator is dedicated to the refrigerator and supplies just enough wattage to run the refrigerator. There's not enough output to run additional stuff, so it doesn't power any of the other outlets. Adding batteries will keep the refrigerator running longer without shore power, but that's all.
If you want to use your batteries for other outlets, you'll probably have to add a separate inverter and sub-panel. The additional inverter would supply power to the sub-panel and you would move some of your circuit breakers into the sub-panel to manage the other outlets that you want hot. And of course you'd also have to have a connection between main breaker panel and sub-panel, with another transfer switch to switch the sub-panel between shore power and battery power. I think there may be combination devices available that include the sub-panel, inverter, and transfer switch.
A simpler, but less elegant solution, would be to add the 2nd inverter and use it to power a single outlet that takes power only from the inverter. When you want to run a 120V appliance, you'd just plug into that outlet.