We have developed a 10- and 14-band anticrossing (BAC) models to investigate the band structures of dilute nitrides and dilute bismides alloys. In fact, the addition of Bi or N to III-V semiconductors causes a significant reduction in the band gap energy and an enhancement of the spin-orbit splitting energy. Further, the conduction and valence offsets between III-V-N/III-V-Bi were also investigated for different nitrogen and bismuth concentrations. For III-V-N/III-V-Bi heterojunctions, the strain-balanced criteria were undertaken by the zero stress analysis. The band alignment of strain-balanced GaAsN/GaAsBi, InPN/InPBi and InAsN/InAsBi is a type II. For InSbN/InSbBi heterostructure, the band lineup can be type I or II.