A recently developed model for homoepitaxial growth on a singular surface in the presence of a Schwoebel barrier at an island edge is extended to the case of heteroepitaxy (without lattice mismatch) by introducing different adatom mobilities in the first layer (heterodiffusion) and in all the next ones (self-diffusion).The model consists of an infinite set of rate equations for adatom and 2D island areal densities and coverage in successive layers. Growth behaviour depending on the model parameters is studied with emphasis on the transient growth regimes: layer-by-layer (LL) to a smooth multilayer (SML) and SML to a rough 3D growth. It is shown that a slower heterodiffusion relative to the self-diffusion leads to a smoother initial growth and thus retards the LL → SML growth trasition, whereas a faster heterodiffusion leads to a rougher initial growth and assists that transition and especially SML → 3D growth transitition at a higher Schwoebel barrier. It is found also that in a smooth growth regime nucleation kinetics eventually acquires a universal scaling form and the corresponding exponents are determined.