The surface of metal-organic vapor-phase epitaxy (MOVPE) grown CuPtB-type ordered (GaIn)P epitaxial layers and their interface to the GaAs substrate have been investigated using high-resolution transmission electron microscopy (HRTEM). We find the (GaIn)P surface to consist of bunched supersteps, (001) terraces, and vicinal regions. The dependence of the height and the density of supersteps, the portion of monolayer steps contained in supersteps as well as the density of antiphase boundaries on the growth temperature and the substrate misorientation is investigated. By comparing the densities of the supersteps and the antiphase boundaries on the (GaIn)P surface and at the interface to GaAs, we find that the supersteps at the interface are the preferential formation site of antiphase boundaries in (GaIn)P. The correlation is disturbed, however, by the effect of the width of supersteps and (001) terraces and of the existence of vicinal regions on the APE formation.