Abstract We present an epitaxial growth model in which a random occupation of substrate lattice sites is assumed before the completion of each layer in layer-by-layer growth. The atomic pair correlation function of the combined adsorbate and substrate system is evaluated. Based on this correlation function we have calculated in closed-form the backscattered electron diffraction beam profile as a function of coverage in the kinematic approximation. We show that the diffracted beams do not broaden but the intensity oscillates as a function of the layer thickness. Realistic applications of this model are discussed.