We report on high-speed metal-semiconductor-metal (MSM) resonant cavity enhanced photodetectors based on Schottky-contacted (Al,In)GaAs heterostructures containing both electron and hole quantum wells. Interdigitated detectors were fabricated and characterized with and without an underlying Distributed Bragg Reflector (DBR). All detectors had very low dark currents and high linear responsivities. The fastest measured temporal response with a 16 ps full-width at half-maximum and a 29 ps fall time was demonstrated on a device with 1 μm gap between electrodes and an underlying DBR. Single quantum well detectors have previously demonstrated increased responsivity and speed but were limited by a slow decaying tail in the high speed photoresponse, attributed to the long collection path of minority carriers. The use of an electron and hole well, separated by a 110 nm absorption region as well as an …