The total energy distribution and the Fowler-Nordheim preexponential factor have been measured for field emission from the (100) and (111) facets of tungsten in the absence and in the presence of overlayers of chemisorbed copper. It is found that at close to monolayer coverage on the (100) facet the adsorbate dramatically reduces the surface density of states at the Fermi energy, whereas on the (111) facet the surface density of states at the Fermi energy is little affected. Self-consistent, semirelativistic LMTO calculations of the k-resolved layer densities of states at the centre of the surface Brillouin zone have been carried out for a tungsten-vacuum interface with and without an ordered overlayer of copper. According to the calculations, a copper monolayer on W(100) strongly suppresses the surface density of states at the Fermi energy, whereas for a copper monolayer on W(111) no such suppression is predicted. The consistency of these results with the experimental data indicates the promise of the present method for calculating the electronic structures of metal-vacuum interfaces.