Recently developed kinetic model for homoepitaxial growth is extended to the case of heteroepitaxy (without lattice mismatch) by introducing different adatom surface mobilities in the first layer (heterodiffusion) and in all the next layers (self-diffusion). With this model the effect of two adatom mobilities as a function of the Schwoebel step-edge barrier is studied with an emphasis on the growth mode transitions. It is shown that the difference between homo- and heteroepitaxy is concerned to the first few monolayers and is crucially sensitive to the ratio between the hetero- and self-diffusion coefficients: lower heterodiffusion coefficient with respect to that of self-diffusion improves essentially epitaxial growth and vice-versa. This is important for growing smooth ultrathin layers needed in modern nanotechnology. Island density kinetics in successive growing layers is studied and it is found that in smooth growth regime it acquires eventually (after deposition approx. 10 monolayers) a universal scaling form and corresponding scaling exponents have been determined.