In the picture of DHumphrey as in Max's Batplane at first glance, there seems to be a Bell X-2 as a background.
But clearly in the Batplane you can see the air inlets for the jet propulsion in the wing deployment, it is bigger to house the crime lab and the television (very important this last, in world cup season)
And the photo of DHumphrey apparently no air intake, could say is a rocket plane ... like the X2, but with two rockets, one on top of the other.
The two engines without air intake led me to the Saunders-Roe SR.53.
which has a rocket motor (de Havilland Specter) and a jet propulsior (Armstrong Siddeley Viper)
Personally I think the Batplane have better design of air intakes than the Saunders-Roe SR.53.
As always I was beaten at the last minute by James.
It happens to me to talk like the batman villains