Hybrid organic−inorganic halide perovskites have sub-band-gap absorption and photocurrent spectra which are difficult to explain using existing models, particularly in light of the small Urbach energies of the intraband absorption edges. Here, we show that the sub-band-gap optical transitions are mediated by bistable amphoteric native defects and a single localized acceptor-like defect strongly coupled to the local lattice vibrations. The coupling is very well accounted for by configuration coordinate diagrams for the defect and for the conduction and the valence band states. The model identifies the common origin of, and uses a single set of parameters to explain, the intricate and very broad bipolar photocurrent spectra found in MAPb(I 1−x Br x ) 3 alloy based photovoltaic (PV) devices, the featureless monopolar photocurrent in MAPbI 3 , and the broad infrared photoluminescence in MAPBr 3 films. In addition, the same deep acceptor defect facilitates, via a multistep process, thermally activated nonradiative recombination of the photoexcited electrons and holes.