Copper thiocyanate (CuSCN) and copper selenocyanate (CuSeCN) combine a high work function with a high optical transparency. To elucidate their potential as transparent hole selective materials, herein, first-principles calculations of the structural and electronic properties are reported, with special attention to the band offsets with crystalline Si and hybrid perovskites (CH3NH3PbI3, CH3NH3PbBr3, and CHN2H4PbBr3). The structural parameters and electronic band structure are obtained using the Perdew–Burke–Ernzerhof functional, resulting in indirect and direct bandgaps of 2.13 and 1.81 eV for CuSCN and CuSeCN, respectively. The (100) surfaces of the two materials do not feature in-gap states, maintaining the semiconducting nature. Band offsets are determined by the electrostatic potential lineup method using slab calculations. Small valence band offsets of 0.10 eV for CuSCN/Si and 0.08 eV for CuSCN/CH3NH3PbI3 are desirably found, i.e., a promising hole transport layer character of CuSCN for Si and CH3NH3PbI3-based solar cells. Type-II band alignment is obtained for all studied heterojunctions.