Once my eldest son (now 10) knew that there was an alternative to milk ie, soids, he refused to drink it ever again. Not one ounce, ever!
I could never find any good info about this problem anywhere, as babies are supposed to love milk, so I made sure that I gave him plenty of calcium rich foods, like yoghurt, cheese etc. I also gave him the packet food (heinz, farley's etc) and mixed it with milk instead of water. Then I stopped worrying about it!!
If he is eating lots of solids, then his appetite will be adequately satisfied, so there maybe another reason for his waking.
Incidentally, child no 2, was not over-interested in milk once he tried solids either, must be in the genes!
Child no 1 is as fit as a fiddle, so just remember to look at the calcium content of food and try to mix in milk where you can!
Good luck and try not to worry....