So a counter-depth fridge is designed to be flush and shallow, but it is easier to reach in the back. The downside is a family of 6. I am afraid it will be too small. If you have a spare fridge in the garage, it may work, but I would rather see you get a 27 cubic foot like a GE French door that will give the capacity needed in the kitchen for a large family.
Maybe do a 4 door that will keep it more organized?
General Electric PVD28BYNFS Profile Series