Why does milk rise up during boiling? And why doesn't water rise up during boiling?

Milk consists of mostly water and some fats, proteins, lactose and minerals. Milk fat is a mixture of glycerides of fatty acids with a density less than that of the milk serum. The solid fat is dispersed in the serum in the form of small globules. When the milk is heated up, these fat globules rise to the top and at a temperature around their melting point, about 50oC, form a layer of skin on the hot milk. 

The steam bubbles that form within the milk get trapped by this skin and accumulate under it. They grow and coalesce and build up a pressure that eventually raises the skin and makes some of the milk spill over, stirring breaks the skin, releases the pressure and prevents spilling over.