The textbook I use has a lesson on breakfast and lunch menus, and
there was something in it bugging me...
Is it ok to use a food and a drink with the verb eat?
I eat cereal, fruit, and milk in the morning.
I'm switching the verb eat with the verb have for the class tomorrow.
I'm really sure it's wrong. Just want to confirm.
I agree. Most authors would express it differently, with "have".
You could also say, "I eat cereal and fruit in the morning, with a glass of milk."