Lipid bilayers attached to solid surfaces play an important role in bioinspired materials and devices and serve as model systems for studies of interactions of cell membranes with particles and biomolecules. Despite active experimental and theoretical studies, the interactions of lipid membranes with solid substrates are still poorly understood. In this work, we explore, using atomistic molecular dynamics simulations, the equilibrium and stability of a phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine membrane supported on hydroxylated amorphous silica. We reveal two distinct types of thermodynamically stable states, characterized by different widths of the water layer between the membrane and the substrate. In α-states, the membrane is closely attached with the lipid head groups interacting directly with surface hydroxyls; however, because of the molecular level roughness of the amorphous silica surface, there exists an inhomogeneous water layer trapped between the substrate and the membrane. In β-states, the membrane is separated from the silica surface by a water film of ∼2.5 nm in thickness. The thermodynamic equilibrium is quantified in terms of the disjoining pressure isotherm as a function of membrane-substrate separation, which has a double sigmoidal shape with two minima and one maximum, which correspond to the limits of stability of α- and β-states. The thermodynamic properties and bilayer structure are compared with experimental findings and simulation results for relevant systems.