It sounds like you have a three way (120v/12v/propane) refrigerator. congratulations! Not many of them around anymore that includes 12v. Without 12v we have to use propane while traveling which means we have to stop short and turn off the fridge before getting gas. You're oaky with the battery while traveling as Mainah said.
I had one once which had a switch to set for 120v,12v, or propane. If that's your case make sure you turn off the 12v when set up or your RV battery will go dead in a hurry.
Paul & Sheri - Upstate New York - SUN-0258
Amateur Radio KD2KCY - VHF 146.520 MHz
2012 F150 F/X 4, 6cyl EcoBoost, Max Tow pkg
2013 Rockwood 8280WS 5th wheel
2006 Sunline Solaris T-1950