A detailed study on the structure, growth, and morphology of epitaxial Pb layers on Si(111) is presented. Grey et al. already determined the structures of the Si(111)(7 x 7)-Pb and Si(111)(unroofed radical 3BAR x unroofed radical 3BAR)R 30-degrees-Pb(beta) monolayer phases with grazing-incidence x-ray diffraction. Our experimental data mainly support their models. In addition, we show that the Pb sites of the incommensurate unroofed radical 3BAR x unroofed radical 3BAR phase are spatially modulated by the substrate corrugation potential. At higher coverages, the Pb atoms form three-dimensional islands that are either oriented parallel to the Si lattice or slightly twisted. The twist angles are different for the 7 x 7 and unroofed radical 3BAR x unroofed radical 3BAR interfaces and can be understood on the basis of simple geometrical arguments. Also, the morphologies of the thick overlayers are different for the two types of interfaces. We argue that both phenomena can be understood if one assumes that the 7 x 7 and unroofed radical 3BAR x unroofed radical 3BAR interface structures remain preserved after depositing thick overlayers.