There are quite a few types of equation of state and abundant pi-a curves of various lipid monolayers at the air-water or the oil-water interface in the literature. However, it has been a problem to interpret mechanochemical properties of bilayer vesicles from the pi-a information of the monolayer. In fact, even the bilayer surface pressure has not yet been well characterized although the monolayer surface pressure has already been traditionally defined as the lowering in the surface tension from the clean interfacial tension due to the presence of the monolayer. The monolayer-bilayer correspondence problem, therefore, could not be well defined and completely solved despite its importance in practice to apply the monolayer pi-a data to elucidate bilayer vesicle properties. In the present analysis, we thus first define the bilayer leaflet pressure as the intrinsic pressure of the lipid layer-water substrate system. This intrinsic surface pressure should be the same function of the Lipid density and the temperature for both the monolayer at an interface and a leaflet of bilayer vesicles. Therefore, the difference between a leaflet of a bilayer and the monolayer at an interface is merely that the latter, but not the former, exhibits a microscopic interfacial tension between the air or the oil and the lipid layer. We show that the value of this intrinsic pressure agrees with that of the traditional monolayer pressure if the macroscopic and microscopic hydrophobic effect assumes the same magnitude. We conclude that the equilibrium pressure between the monolayer and bilayer vesicles is equal in magnitude to the microscopic interfacial tension between the water and the monolayer, which, in first approximation, is equal to the macroscopic oil-water interfacial tension, i.e., ca. 49 mN/m. This conclusion agrees with that briefly derived by pioneers (Gruen and Wolfe, 1982; Nagle, 1976, 1986; Jahnig, 1984). We further develop from mechanics and thermodynamics of membranes a procedure to obtain either analytically from a theoretical or empirical equation of state, or graphically from the pi-a curve of the monolayer at an interface, mechanochemical properties of this monolayer and bilayer vesicles. The method is exemplified for the monolayer and bilayer vesicles of dilauroyl phosphatidylethanolamine (DLPE).