Stretchable broadband photodetectors (PDs) are attractive for applications in wearable optoelectronics and personal healthcare. However, the development of stretchable broadband PDs is limited by difficulties in obtaining materials, designing device structures, and finding reliable fabrication processes. Here, we report stretchable broadband PDs by forming organic-inorganic vertical multiheterojunctions on a three-dimensionally micro-patterned stretchable substrate (3D-MPSS). The stress-adaptable 3D-MPSS structure allows all layers of the PD coated on it to sustain tensile strains. Generation of photovoltage in the vertical hybrid structure of PbS quantum dots/ZnO nanorods as a photo-responsive material on poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) as a transport channel is considred to be the mechanism of the device response to UV-Vis-NIR. The fabricated PDs present responsivity to UV (365 nm), Vis (565 nm and 660 nm), and NIR (880 nm and 970 nm) light, as well as reliable electrical performance under applied stretching up to 30%.