The correct statement is "be careful not to let the milk boil over" (not to let it boil over and mess up the stove)

There are two ways that I would say this depending on what you mean to say: Be careful not to over boil the milk. (If you "over boil" milk you have boiled it too much and now it tastes bad.) Be careful not to let the milk boil over. ("Boil over" is when the milk boils so much that it goes over the side of the saucepan.) The syntax of your original sentence is a bit strange. We wouldn't usually put "with the milk" in the middle of the sentence in writing (though people might say it verbally). The order of the words "boil" and "over" definitely change the meaning though!

Be careful with the milk not to over boil.