Molecular dynamics simulations of 1,2-di-O-acyl-3-O-β-D-galactopyranosyl-sn-glycerol (MGDG) and 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) bilayers were carried out to compare the effect of the lipid head group's chemical structure on the dynamics and orientational order of the water molecules hydrating the bilayer. The effect of the bilayers on the diffusion of water is strong for the neighbouring water molecules i.e., those located not further than 4 Å from any bilayer atom. This is because the neighbouring water molecules are predominantly hydrogen bonded to the lipid oxygen atoms and their mobility is limited to a confined spatial volume. The choline group of DOPC and the galactose group of MGDG affect water diffusion less than the polar groups located deeper in the bilayer interface, and similarly. The latter is an unexpected result since interactions of water with these groups have a vastly different origin. The least affected by the bilayer lipids is the lateral diffusion of unbound water in the bilayer plane (x,y-plane) - it is because the diffusion is not confined by the periodic boundary conditions, whereas that perpendicular to the plane is. Interactions of water molecules with lipid groups also enforce certain orientations of water dipole moments. The profile of an average water orientation along the bilayer normal for the MGDG bilayer differs from that for the DOPC bilayer. In the DOPC bilayer, the ordering effect of the lipid head groups extends further into the water phase than in the MGDG bilayer, whereas inside the bilayer/water interface, ordering of the water dipoles in the MGDG bilayer is higher. It is possible that differences in the profiles of an average water orientation across the bilayer in the DOPC and MGDG bilayers are responsible for differences in the lateral pressure profiles of these bilayers.