Symmetry breaking has a crucial effect on electronic band structure and subsequently affects the light-absorption coefficient of monolayers. We systematically report a family of two-dimensional (2D) Janus transition-metal nitride halides (TNHs, T = Ti, Zr, Hf, Fe, Pd, Pt, Os, and Re; H = Cl and F) with breaking of both in-plane and out-of-plane structural symmetry. The dynamical, thermal and mechanical stabilities are calculated to check the stability of the Janus TNHs. The electric properties of ten TNHs are studied via the HSE06+SOC method and the band gaps range from 0.93 eV (PdNCl) to 4.74 eV (HfNCl). Desirable light adsorption coefficients of up to 105 cm-1 are obtained for the Janus TNHs with no central symmetry. The Janus OsNCl monolayer shows excellent electrical transport properties and ultrahigh carrier mobility (104 cm2 V-1 s-1). Heterojunctions formed by stacking two Janus TNH monolayers are further investigated for solar cell applications. Eight of the heterojunctions have type-II band alignments. Surprisingly, the OsNCl/FeNCl heterojunction has a power conversion efficiency (PCE) of 23.45%, which is a larger value compared to the PCE of GeSe/SnSe heterostructures (21.47%). The optical properties and the built-in electric field of the OsNCl/FeNCl heterojunction are investigated. These results indicate that the stable Janus TNH monolayers have potential applications in photoelectric devices, and the vertical heterojunctions can be used in solar cells.