It's not normal for any human being to keep ingesting milk past weaning from his or her mother's breast. I say this as somebody who is apparently not weaned, since I can't give up cheese and yogurt. It's normal for us to lose the lactase that allows us to digest lactose. There was a mutation among some Europeans way back when that allowed them to keep digesting dairy -- which was a helluva survival advantage to them. Depending on your ancestry, you're more or less likely to be able to digest lactose all your life.

When my daughter really wants to eat a dish with milk in it, she takes Lactaid and that works relatively well for her.