Question

The layer of the earth we stand on and that is only a few miles thick

Answer 1

This is called the crust: oceanic crust is around 5 km (3 miles) to 10 km (6 miles ) thick and the continental crust is 20 to 30 miles thick, (still, i think that the word you're looking for is "crust" or "oceanic crust" to be sure.