The Ono–Kondo lattice model for the density gradient near a surface is applied to surfaces where the adsorbate–adsorbent interactions are not homogeneous. While solving the general equations would be quite complex, relatively simple solutions can be obtained for periodic surfaces such as a checkerboard. It is shown that the adsorption behavior on surfaces with molecular-scale heterogeneities is very different from adsorption on surfaces where the surface heterogeneities are much larger than the size of the adsorbent molecules.