The physical properties of lipid bilayers can be remodeled by a variety of environmental factors. Here we investigate using molecular dynamics simulations the specific effects of nanoscopic substrates or external contact points on lipid membranes. We expose palmitoyl-oleoyl phosphatidylcholine bilayers unilaterally and separately to various model nanosized substrates differing in surface hydroxyl densities. We find that a surface hydroxyl density as low as 10% is sufficient to keep the bilayer juxtaposed to the substrate. The bilayer interacts with the substrate indirectly through multiple layers of water molecules; however, despite such buffered interaction, the bilayers exhibit certain properties different from unsupported bilayers. The substrates modify transverse lipid fluctuations, charge density profiles, and lipid diffusion rates, although differently in the two leaflets, which creates an asymmetry between bilayer leaflets. Other properties that include lipid cross-sectional areas, component volumes, and order parameters are minimally affected. The extent of asymmetry that we observe between bilayer leaflets is well beyond what has been reported for bilayers adsorbed on infinite solid supports. This is perhaps because the bilayers are much closer to our nanosized finite supports than to infinite solid supports, resulting in a stronger support-bilayer electrostatic coupling. The exposure of membranes to nanoscopic contact points, therefore, cannot be considered as a simple linear interpolation between unsupported membranes and membranes supported on infinite supports. In the biological context, this suggests that the exposure of membranes to nonintercalating proteins, such as those belonging to the cytoskeleton, should not always be considered as passive nonconsequential interactions.