I have freezed both milk and cheese for years without a problem. With freezing milk you need to take a couple of glasses out of the top of the container before freezing otherwise it will expand and make a BIG hard to clean up mess when it freezes. With cheese, I use a relatively hard cheese–sharp cheddar I have found to work the best personally, and wrap it very securely in plastic wrap and then freezer paper over the plastic wrap.
With the cheese once it is thawed I grate it up for salads, tacos, etc with out a problem. I have also frozen cheese that is sliced but individually wrapped. When it is thawed nobody has noticed a difference from the frest cheese.
Nobody ever noticed a difference in the milk either!