There are a couple ways to do this.
One issue is how to hook the new, battery based inverter to the loads. Were you thinking of just running an extension cord(s) into the house? That would be one way to do it. You could have a whole separate combiner box, charge controller, battery bank, and inverter, at the pole, and in the event of disaster unplug each panel from its microinverter, and plug them into the wires that lead to the new combiner box. One issue would be keeping the batteries charged in between disasters. You could have a AC trickle charger for that.
The other way to do it is an "AC Coupled" system, where there is an inverter which gets wired in between some or all of the microinverters and the grid, and a critical loads subpanel. When the grid is up, the whole system works as now, when the grid goes down, the inverter has a transfer switch which disconnects from the grid, and the output of this inverter keeps the microinverters running. This probably would require some rewiring of the house to create that critical loads subpanel. It is a little counter intuitive how the whole thing works, there are some documents online if you want to pursue it.