You can find this described many places, and you will find many places (including technical references both old and new) where the term "air over hydraulic" is used incorrectly.
Deuce brakes are hydraulic brakes as far as any governing body is concerned. More specifically, they are power assisted hydraulic brakes. More specifically than that, they are air assisted hydraulic brakes. But they are hydraulic. The "air" need not be specified any more than the vacuum assist needs to be specified on your car, or the hydraulic assist needs to be specified on your diesel pickup truck.
First and foremost, let me say that these are way oversimplified and generalized....
With hydraulic brakes, the pedal is directly connected to a hydraulic cylinder (the master cylinder) and the force applied to the pedal is transferred by the fluid directly to the slave cylinders (wheel cylinders) where it is converted back to mechanical motion.
With assisted hydraulic brakes, this remains the same, however there is a power assist device. In most modern stuff, this device applies additional force to the mechanical linkage between the pedal and the master cylinder that is far more but directly proportional to your input force. More common in days gone by, and on deuce and a halfs in particular, an "inline" type booster is used, where the assist is added after the master cylinder and before the wheel cylinders.
With full air brakes, the treadle valve (brake pedal) operates a variable air pressure regulator. This pressurizes the air line to each wheel, where the air acts on a diaphragm, the diaphragm then operates a fully mechanical brake. Most commonly with a rotating "camshaft" that spreads the shoes as it rotates. Another common type is simply a wedge that is perpendicular to the direction of the brake shoes, and as the wedge is driven between them, the shoes expand.
With air over hydraulic brakes, you essentially have two complete braking systems. It starts as full air, in that you have a treadle valve in lieu of a brake pedal, when you step on the brakes you control only air. This part of the system is identical to full air brakes. The air then instead of branching to a diaphragm at each wheel, will simply act on a single diaphragm. That diaphragm is attached to a brake master cylinder of a completely independent hydraulic brake system. From that master cylinder, fluid pressure is applied to hydraulic wheel cylinders to activate the brakes. Virtually two full complete braking systems, with the first one serving only to activate the second one. This is not what is present on the deuce and a half. The M105 "deuce trailer" does use a true air over hydraulic braking system. You only hitch up an air line, the air runs the hydraulics.