The linear muffin-tin orbitals method in the atomic-sphere approximation is employed to investigate the electronic structure of a semiconductor-metal interface at monolayer coverage. We studied the interface formed by one monolayer of Na adsorbed on Si(111). Analysis of both valence- and core-electron states gives information on the nature of the bond between Na and the Si surface, which is mainly covalent, and allows one to interpret the available experimental data.