We propose a new approach in device architecture to realize bias-selectable three-color shortwave-midwave-longwave infrared photodetectors based on InAs/GaSb/AlSb type-II superlattices. The effect of conduction band off-set and different doping levels between two absorption layers are employed to control the turn-on voltage for individual channels. The optimization of these parameters leads to a successful separation of operation regimes; we demonstrate experimentally three-color photodiodes without using additional terminal contacts. As the applied bias voltage varies, the photodiodes exhibit sequentially the behavior of three different colors, corresponding to the bandgap of three absorbers. Well defined cut-offs and high quantum efficiency in each channel are achieved. Such all-in-one devices also provide the versatility of working as single or dual-band photodetectors at high operating temperature. With this design, by retaining the simplicity in device fabrication, this demonstration opens the prospect for three-color infrared imaging.