What is the proper glue to use to bond two pieces of plywood together as a substrate for formica?
I don't think it's going to be critical but when in doubt: PL. As far as I can tell, PL Premium can bond anything to anything. In a case like this, do a bead around the perimeter and bolts (quarter sized blobs) about 8" inches apart in a grid and you'd have to sacrifice a goat to a powerful deity to get those two pieces of plywood apart. The more important bond to consider is the laminate to your substrate. On that topic, counter tops are made with particle board, not plywood. PB is cheaper, flatter, and free of voids. Go particle board if you can (yes they make it in 3/8"), if not don't worry just make sure your plywood is of very high quality.