Confused on correct way to do this
 

My husband just started driving an 18 wheeler. He drives for a national company so he doesn't own the truck. We need to know best way for him to get power for frig, microwave without connecting to the truck's battery. We think we need a power invertor, a sealed battery. Guess my question is how do we do all this without costing a fortune and how do we recharge the sealed battery. Any advice would be helpful

is the fridge 110 vac or 12vdc ? they make duel voltage units.

imo the thermo electric units aren't worth the "savings" - they run NON stop and don't cool very well.

they only way to power a 110vac appliance is via an DC to AC inverter, or a shore power cord/connection. shore power don't do you any good if you're not parked.

done properly, you'll want to isolate the battery/supply from the engine batteries (to prevent running the engine/starting batteries down) - this is done w/ a ISOLATION relay, which allows the "fridge" battery to be charged when the engine is running, yet isolated the batteries from the engine/start batteries when the engine is turned off.

a microwave cab be a huge wattage drawl - you're gonna need a good size inverter & batteries to run it and you might not be able to run anything else when running the microwave.

i think space in the truck is gonna determine how big a fridge / microwave you have & from there you can determine how large an inverter you'll need.

its no secret that I'm a fan of the EdgeStar, ARB, Engel & Dometic - they're expensive but they work better than any thermoelectric and they'll last a LOT longer - my EdgeStar has been running (non stop) for over 3 years & I have a friend that has one in his van thats been plugged in for over 4 years.

As for the fridge I think you could use a inverter couldn't you? I bet the largest one you can plug into a standard cigarette lighter socket would power a small fridge. I agree with Don on the thermal electric types not being very good. But, they will withstand a lot of abuse and vibration. And, they're pretty inexpensive. My son was in a similar situation a few years ago when he drove a company truck. We took the passenger seat out and strapped down the fridge there. We wired the inverter directly to the battery bank. Sounds like you might need to switch trucks or the company won't allow such a changes? He broke a few of those standard motorized type dorm fridges I think because of all the bouncing. We switched over to a thermal electric type and that lasted.
As Don said, the microwave is going to need a lot of power. I don't know if you'll be able to run it through the cig lighter inverter. What about getting the smallest Honda generator you can get with a remote starter and strapping (and locking) it to the catwalk outside? Not going to be inexpensive, but should be pretty slick. If you mount it in some sort of protective box it'll keep it in better shape so it will hold value longer. And keep thieves eyes off it.