The best I can do is that the zener + diode sets the junction of the bases to 1/2 of Vcc. The diode is for temperature compensation. In the absence of pulses from Aout, both the BJTs are off, the top one conducts when its base is at 1/2Vcc +.8, the bottom when its base is at 1/2Vcc -.8. AS Aout has a finite rise and fall times to its edges, this gives a dead band around 1/2Vcc where both BJTs are off. The effect is that the output at the emitters is a pulse that starts later and finishes earlier then Aout. Its more protection against the top FETs being on when the bottom FETs are on.
Frank