We propose an integrated molecular/continuum thermodynamic model for calculating electrostatic contributions to the free energy of hydration that is based on a correlation function expansion of the free energy. The model uses explicit water simulation results for simple monatomic and diatomic solutes to calculate lower order correlations in this expansion and systematically corrects for higher order correlations using the continuum description of hydration. The model is applied to calculating free energies of charging the tetramethylammonium (TMA) ion and idealized TMA-like solutes in water. We find that the effects of water structure on ion hydration are embodied in the lower order correlations and, thus, are accounted for by the explicit water simulation results. In addition, continuum corrections for higher order correlations are found to be independent of the Born radii chosen for oppositely charged ions. Thus, the model reduces the reliance of the continuum description on parametrization of the Born radii.