Although sulfide perovskites usually require high-temperature syntheses, we demonstrate that organosulfides can be used in the milder syntheses of halide perovskites. The zwitterionic organosulfide, cysteamine (CYS; +NH3(CH2)2S-), serves as both the X- site and A+ site in the ABX3 halide perovskites, yielding the first examples of 3D organosulfide-halide perovskites: (CYS)PbX2 (X- = Cl- or Br-). Notably, the band structures of (CYS)PbX2 capture the direct bandgaps and dispersive bands of APbX3 perovskites. The sulfur orbitals compose the top of the valence band in (CYS)PbX2, affording unusually small direct bandgaps of 2.31 and 2.16 eV for X- = Cl- and Br-, respectively, falling in the ideal range for the top absorber in a perovskite-based tandem solar cell. Measurements of the carrier dynamics in (CYS)PbCl2 suggest carrier trapping due to defects or lattice distortions. The highly desirable bandgaps, band dispersion, and improved stability of the organosulfide perovskites demonstrated here motivate the continued expansion and exploration of this new family of materials, particularly with respect to extracting photocurrent. Our strategy of combining the A+ and X- sites with zwitterions may offer more members in this family of mixed-anion 3D hybrid perovskites.