An accurate description of the structure and dynamics of interfacial water is essential for phospholipid membranes, since it determines their function and their interaction with other molecules. Here we consider water confined in stacked membranes with hydration from poor to complete, as observed in a number of biological systems. Experiments show that the dynamics of water slows down dramatically when the hydration level is reduced. All-atom molecular dynamics simulations identify three (inner, hydration and outer) regions, within a distance of approximately 1 nm from the membrane, where water molecules exhibit different degrees of slowing down in the dynamics. The slow-down is a consequence of the robustness of the hydrogen bonds between water and lipids and the long lifetime of the hydrogen bonds between water molecules near the membrane. The interaction with the interface, therefore, induces a structural change in the water that can be emphasized by calculating its intermediate range order. Surprisingly, at distances as far as ~ 2.5 nm from the interface, although the bulk-like dynamics is recovered, the intermediate range order of water is still slightly higher than that in the bulk at the same thermodynamic conditions. Therefore, the water-membrane interface has a structural effect at ambient conditions that propagates further than the often-invoked 1 nm length scale. Membrane fluctuations smear out this effect macroscopically, but an analysis performed by considering local distances and instantaneous configurations is able to reveal it, possibly contributing to our understanding of the role of water at biomembrane interfaces.