A recently developed lattice field theory formulation of the statistical mechanics of a classical Coulomb gas interacting with a fixed charge distribution [R. D. Coalson and A. Duncan, J. Chem. Phys. 97, 5653 (1992)] is extended to deal with systems having a spatially varying dielectric constant. To illustrate the utility of the formalism, electrostatic free energies of two oppositely charged macroions suspended in ionic solution are calculated for several geometric configurations. In many cases, it is found that the free energy is minimized at a separation between macroions corresponding to a "nontouching" configuration. The value of the dielectric inside the macroions has an important effect on the free energy of near-touching configurations. In particular, lowering the dielectric constant inside the macroion relative to the solvent dielectric constant leads to higher free energies of near-touching configurations, and hence promotes a stable state where the macroions are farther apart. Our findings also indicate that a large difference between the magnitude of the charges on the positive and negative macroions enhances the stability of a "nontouching" configuration.