My son is the same way. You can substitute soy milk or rice milk for milk. You can use dairy-free margarine for butter (Nucoa, Earth's Balance, Best Life are all good brands, but read the labels to be 100% sure. Look for words like whey, casein, caseinate in addition to milk, milkfat, milk solids, etc)
For eggs, you can use the following mixture to substitute for each egg in a recipe:
1.5 TBSP oil
1.5 TBSP water
1 tsp baking powder
mix all three together, then add to the recipe where you would normally add the eggs. Double for two eggs
With those, you can turn almost any regular recipe into an allergy friendly one. For cheese, Tofutti makes good sliced cheese and Follow Your Heart makes good cheese for melting (though neither is as good as the real thing, of course). Many brands of soy cheese still contain milk proteins, so make sure you're careful (the above mentioned brands are safe).
Two good cookbooks that I highly recommend:
http://www.amazon.com/Milk-Free-Egg-Free-Nut-Free-Allergy...
http://www.amazon.com/Food-Allergy-Mamas-Baking-Book/dp/1...
(note: the brownies in the first book come out very crumbly. I don't recommend them)
Ghiradelli brand semi sweet chocolate chips are dairy free.
Great blog (by author of the second cookbook): http://www.foodallergymama.com/