It's about 2" high. We made the decision on the height based on other elements in the kitchen. In this case - we didn't want a thin strip of paint between the backsplash and window trim. The other walls in the kitchen have a tile backsplash that extends down to the countertop. It didn't make sense to use tile on this wall so we wanted to minimize the splash but still provide a finished look that protects the wall and back of cabinets from spills.

is it the normal thickness of the granite? or milled down thinner?

It is the normal thickness of granite.