The electronic structure of a Pb overlayer on Ag(111) has been studied by angle-resolved photoemission spectroscopy. We identify three p bands. While the p(xy) bands are sharp and closely resemble the corresponding bands of a free-standing Pb layer, the p(z) band is strongly spread in energy and momentum. Tight-binding calculations of the electronic structure combined with structural calculations using the embedded atom method indicate a symmetry dependent hybridization with the Ag(111) surface. We propose a symmetry selective, surface state mediated coupling to the bulk continuum which results in a broadened line shape for the p(z) band only.