The electrostatic interaction of charged spherical colloids trapped at an interface between a nonpolar medium and water is analyzed. Complementary experiments provide consistent values for the dipole-dipole interaction potential over a wide range of interparticle distances. After accounting for the contribution from the compact inner double layer arising from the finite size of the counterions, we demonstrate quantitative agreement between experiments and nonlinear Poisson-Boltzmann theory. We find that the inner layer contribution dominates the electrostatic interaction in the far field for particles pinned at the interface. This result is fundamentally different from screened electrostatic interactions in the bulk and could contribute to the further understanding of the structure of the compact counterion layer in highly charged systems.