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.