The free energy of adhesion per unit area (hereafter referred to as the adhesion strength) of lipid arrays on surfaces is a key parameter that determines the nature of the interaction between materials and biological systems. Here we report classical molecular simulations of water and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid bilayers at model silica surfaces with a range of silanol densities and structures. We employ a novel technique that enables us to estimate the adhesion strength of supported lipid bilayers in the presence of water. We find that silanols on the silica surface form hydrogen bonds with water molecules and that the water immersion enthalpy for all surfaces varies linearly with the surface density of these hydrogen bonds. The adhesion strength of lipid bilayers is a linear function of the surface density of hydrogen bonds formed between silanols and the lipid molecules on crystalline surfaces. Approximately 20% of isolated silanols form such bonds but more than 99% of mutually interacting geminal silanols do not engage in hydrogen bonding with water. On amorphous silica, the bilayer displays much stronger adhesion than expected from the crystalline surface data. We discuss the implications of these results for nanoparticle toxicity.