Three-dimensional (3D) hybrid perovskites CH3NH3PbX3 (X = Br, I) have recently been suggested as new key materials for dye-sensitized solar cells (DSSC) leading to a new class of hybrid semiconductor photovoltaic cells (HSPC). Thanks to density functional theory calculations, we show that the band gap of these compounds is dominated by a giant spin-orbit coupling (SOC) in the conduction-band (CB). At room temperature, direct and isotropic optical transitions are associated to a spin-orbit split-off band related to the triply degenerated CB of the cubic lattice without SOC. Due to the strong SOC, the electronic states involved in the optical absorption are only slightly perturbed by local distortions of the lattice. In addition, band offset calculations confirm that CH3NH3PbX3/TiO2 is a reference material for driving electrons toward the electrode in HSPC. Two-dimensional (2D) hybrids are also suggested to reach further flexibility for light conversion efficiency. Our study affords the basic concepts to reach the level of knowledge already attained for optoelectronic properties of conventional semiconductors.