We present a second nearest neighbor semi-empirical sp(3)s* tight binding model to calculate the electronic band structure of nitride/arsenide or phosphide heterostructures. The sp(3)s* model Hamiltonian includes the spin-orbit coupling of p-states, second nearest neighbor (2NN) atomic interactions. Atomic energy levels and bond lengths of ternary semiconductors are taken as nonlinear function of alloy composition. The model findings for InAsN/InAs, GaPN/GaP and GaAsN/GaAs structures are in excellent agreement with experiment for the band gaps at I, L and X symmetry points. It is found that the bulk band structure properties and lattice mismatch strain have significant effects on band offsets and GaPN/GaP, InAsN/InAs and GaAsN/GaAs heterostructures are type II for small composition (0.0 < x < 0.50) and become type I for large composition 0.50 < x < 1.0. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.