The structure of the solid-liquid interface is of fundamental importance in chemistry, but progress in understanding this interface has been slow, due to the lack of in-situ probes that provide information at atomic scales. Recently, in-situ surface x-ray scattering measurements have provided insight into the microscopic nature of solid-liquid interfaces and this paper discusses experiments on electrochemically deposited monolayers of Pb, Tl, and Bi on Ag and Au (111) electrodes. Tl and Pb form 2-D, incommensurate hexagonal solids that are compressed relative to bulk and rotated by 4 - 5 degree(s) with respect to the substrate. As the applied electrode potential decreases, the in-plane atomic spacing also decreases, since the chemical potential of the monolayer increases. From these data, the 2-D compressibility of the monolayer can be calculated. We find that the compressibility is only slightly dependent on substrate, being smaller on Ag(111) than on Au(111). For Tl/Ag(111), the intensity of the Ag surface diffraction changes when the monolayer is adsorbed. This results from a substrate- induced modulation of the atomic positions in the incommensurate monolayer and we have quantified this modulation. Bi/Ag(111) forms an unusual structure: a rectangular lattice that is uniaxially commensurate with the hexagonal surface. There are two Bi adatoms per rectangular unit cell and one adatom is displaced from the centered position by 0.35 angstrom. The commensurate Bi rows lie along the rows of threefold hollow sites on the Ag(111) surface. This unusual structure reflects the tendency toward covalent bonding found in Bi and a fortuitous match between the atomic spacings of the Ag substrate and the close packed planes of bulk Bi. In contrast to Tl and Pb where the compressibility is isotropic, Bi/Ag(111) compresses anisotropically and this maintains the uniaxially commensurate structure. Our results show that for these metal monolayer systems the adatom-adatom interactions determine the atomic structure of the monolayer and the adatom-substrate interactions only weakly affect this structure. Furthermore, the structure is not influenced by the presence of the large concentration of adsorbed water molecules or anions.