What happens when you mix milk and coke? Add small amounts of milk to a bottle of coke, and you end up with a white-ish precipitate with a clear liquid on top. "The Internet" seems to agree that phosphoric acid in coke reacts with something in the milk (possibly proteins, it seems to me). The Telegraph even wrote that it is the "milk molecules" that react.

So what is the reaction(s) that takes place?  I can't find any proper sources that explain this in chemical terms.

Telegraph's milk-molecule analysis: 
 This is what happens when you add milk to coke
or via the Internet Archive (without pictures).
The phosphoric acid causes denaturation of milk proteins which precipitate out of the solution (milk is an emulsion, to be exact). The flock that is formed also adsorbs dye molecules (caramel) which is why the solution become clear.

There is nothing coke-specific about it. Any acid would denature milk just like that. And nearly any huge organic molecule would get absorbed, just like caramel dye.