Half H-bridge using only ntype mosfets or npn transistors
You can make an H bridge with devices of all the same polarity. 

However the problem comes with driving the control terminals. This is usually solved by using the switching action of the bridge itself to generate a 'bootstrap' rail. In the case of N-ch FETs, this would typically be 15v above the most positive power rail to drive the upper gates fully. Using P-ch for the upper devices avoids this (slight) complication.