Any sort of hybrid system is of minimal benefit on an aircraft and probably not worth the weight. The big advantage of hybrid for cars (and trucks) is regenerative braking - eliminating much of the penalty in stop/go driving. Any use of the friction brakes is lost efficiency that you can't get back.
Aircraft use a lot of energy climbing to cruise altitude, but they get most of that back when they throttle back for descent. If properly planned, very little fuel is used in the last ~100 miles of a typical flight since the engines are at idle from top of descent until they start setting up for approach and landing. The only time regenerative braking could be used is during landing, and the potential energy recover is too small to compensate for the weight of the needed hardware on any but the shortest range flights.
Bottom line, unless there is massive breakthrough in battery energy density, aviation will remain dependent on hydrocarbon based fuels for other than short range operations (hydrogen is light, but it's energy density is horrible - combined with it's inherent packing difficulties it's also unsuitable for long range aircraft). We might be able to make the hydrocarbon based aviation fuels renewable and carbon neutral, but there is no current or foreseeable technology that has the realistic ability to replace it.
Edit: I see Flightless Parrot has posted pretty much the same thing while I was composing mine.