Understanding the electronic properties of dopants near an interface is a critical challenge for nanoscale devices. We have determined the effect of dielectric mismatch and quantum confinement on the ionization energy of individual acceptors beneath a hydrogen passivated silicon (100) surface. While dielectric mismatch between the vacuum and the silicon at the interface results in an image charge which enhances the binding energy of subsurface acceptors, quantum confinement is shown to reduce the binding energy. Using scanning tunneling spectroscopy we measure resonant transport through the localized states of individual acceptors. Thermal broadening of the conductance peaks provides a direct measure for the absolute energy scale. Our data unambiguously demonstrates that these two independent effects compete with the result that the ionization energy is less than 5 meV lower than the bulk value for acceptors less than a Bohr radius from the interface.