We have grown ZnSe epitaxial layers on bulk GaAs substrates and on GaAs epitaxial layers, with both As-rich and Ga-rich surface terminations. We have also grown ZnSe on AlAs epitaxial surfaces with different As to Al ratios. In all cases, abrupt, layer-by-layer growth is observed on the As-rich surfaces, while 3-dimensional nucleation is observed on the group III-rich surfaces. GaAs was also grown on ZnSe layers. In this case, microtwins form at the interface whose density diminishes as the layer is made thicker. A growth model is proposed consistent with these results which requires over-all electronic balance at the interface.