M.,
I don't want to scare you, but let me share what happened to my best friends' kids.
She also laid them down with milk sippy cups at night. Aside from ear infections, their teeth got so bad that her daughter had to have all six of her molars removed, and her son had to have three molars and both of his front teeth removed. Both were from cavities which got infected when the milk would sit in their mouths overnight (from taking the sippy to bed with them, drinking it, and then not brushing before falling asleep).
She switched them to water, and gradually put less and less in their cup, then began to set it on the bedside table, where they could still access it. Now they are allowed a drink of water before they get in bed, but that's it. You can gradually move away from it, but I'd switch to water immediately. Your son probably won't like the transition, but he's old enough to understand when you tell him "No more milk at bedtime." Expect a few tears, but stick to your guns!
You'll also want to transition away from the cup as soon as possible, as this nocturnal sucking can cause his teeth to shift as well, causing an overbite (from my own experience - I had to have 4 years of braces to correct it).
And just so you know, my son also would wake up and want a drink, I'd give him a small sip of water and put him back to bed. He stopped around 3, if I remember correctly.
So, like I said, I don't want to scare you, but you should probably start weaning him away from a nighttime cup as soon as possible.