How long do you think you can suck 100 amps out a 12v battery? 100a x 12 v = 1200 watts. A frig will require a large amount of power to start. A furnace's biggest load is the fan motor. The modern hi-tech furnaces may not like the inverter voltage. If you have an old oil furnace, it has two motors, blower and gun.
I wouldn't want to stay warm with battery backup.
Personally, I think it's a pipe dream.
Post back if it works.
I think you would be better off with an RV genny. They are quiet, can get 30 amps out of the RV plug. That might work much better and run both furnace and frig providing the furnace likes the wave put out by the genny.
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