We investigate the structure and mechanical properties of glassy water confined between silica-based surfaces with continuously tunable hydrophobicity and hydrophilicity by computing and analyzing minimum energy, mechanically stable configurations (inherent structures). The structured silica substrate imposes long-range order on the first layer of water molecules under hydrophobic confinement at high density (ρ ≥ 1.0 g cm⁻³). This proximal layer is also structured in hydrophilic confinement at very low density (ρ 0.4 g cm⁻³). The ordering of water next to the hydrophobic surface greatly enhances the mechanical strength of thin films (0.8 nm). This leads to a substantial stress anisotropy; the transverse strength of the film exceeds the normal strength by 500 MPa. The large transverse strength results in a minimum in the equation of state of the energy landscape that does not correspond to a mechanical instability, but represents disruption of the ordered layer of water next to the wall. In addition, we find that the mode of mechanical failure is dependent on the type of confinement. Under large lateral strain, water confined by hydrophilic surfaces preferentially forms voids in the middle of the film and fails cohesively. In contrast, water under hydrophobic confinement tends to form voids near the walls and fails by loss of adhesion.