A simple lattice-fluid model is presented for solute adsorption from a bulk liquid onto a solid surface in the presence of an additional thin (liquid) surface coating. In this model, solutes first absorb in this intermediate surface film before they adsorb at the solid surface. This coupling of adsorption with absorption behavior has a significant effect on the overall solute depletion from the bulk liquid. Consequently, the particular choice of surface film can be used to "tune" the adsorbent for particular needs (e.g., this can be used to increase the sorbent selectivity when several solutes are present). In the limit where the solvent in the bulk liquid and the surface coating material are mutually immiscible, the governing equations decouple and reduce to simple Boltzmann laws. In these analytical expressions, the depletion of solute depends linearly on the bulk concentrations, where the proportionality factor reflects the strengths of fluid-fluid relative to fluid-surface interactions. Good agreement is obtained when comparing predictions of the model with Monte-Carlo simulations (based on the same microscopic model).