IMHO, a 3-way fridge that uses a 12VDC heating element is one of the biggest wastes of energy I have ever seen in an RV!
First and most importantly, the 12VDC operation relies on a 12VDC heating element to attempt to replicate the heating found from your 120VAC heating element when connected to shore power. Assuming a 240 watt (they are actually higher) 12VDC heating element, that will draw 20 amps from your battery every hour of operation
It also has a lower heating capacity than the 120VAC element, and will NOT cool the fridge, as it was never designed to do this. It's sole function is to attempt
whatever cold temps are found in the fridge when you start it on 12VDC heating. It has a hard time doing even this!
As for longevity of your battery bank while on 12VDC heating, assuming that you have a newer Airstream with 2 OEM group 24 batteries, you would have a total battery capacity of 160 amp/hours. Since you should only draw that amount down to half, than gives you a useful battery capacity of 80 amp/hours, which translates into just 4 hours of fridge use while on 12VDC.
And don't expect your charge line from your tow vehicle to help much either. Most trailer wiring does not accept much more than 5 amps from the TV.
OTOH, a marine style fridge with a Danfoss compressor system will draw around 3 amps while on 12VDC, and about 1 amp on 120VAC. The numbers are much better (26 hours of continual operation from 80 amp/hours), but it presents you with other problems, like keeping your battery bank charged. Solar is the way to go with a marine fridge!