A bad breath can be caused and associated with so many things you eat sometimes it is not just about what you put in your mouth but could be a system related odour that can be unpleasant to the next person. The breath of milk and cheese brings the most sour mouth taste breath.
Your mouth is the first part of your digestive tract, chewing is only the first step. Think of it as you chewing on so many things and there are millions of bacteria feasting on food particles and tissue in your mouth. It is therefore bound to release such an odour as it releases smelly waste.
Dairy often brings the worst as microbes that work to digest milk solids such as proteins, lactose and lipids tend to create excess hydrogen sulphide, this therefore explains why your mouth smells like a wasted egg after eating cheese. Often time you will see how bacteria gathers itself bellow your gum line, teeth and between your tongue.
However to get rid of this you should consider brushing your teeth with a fluoridated toothpaste at least twice a day and when you feel you have bad exhalations after every meal. In most cases unfortunately mouthwash does not help take away all the gram-negative bacteria, even though it kills all bacteria its function is limited.
Flossing helps as well as good oral hygiene can help fight milk breath. This does not entirely mean you cannot have cheese and milk you still can with the proper hygiene care.