We designed artificial models of biological membranes by deposition of synthetic glycolipid membrane multilayers on planar silicon substrates. In contrast to commonly used phospholipid membranes, this offers the unique possibility to study the influence of membrane-bound saccharide chains (cell glycocalix) on the membrane mechanics. Taking advantage of the planar sample geometry, we carried out specular and off-specular neutron scattering experiments to identify out-of-plane and in-plane scattering vector components. By considering the effects of finite sample sizes, we were able to simulate the measured two-dimensional reciprocal space maps within the framework of smectic liquid-crystal theory. The results obtained both at controlled humidity and in bulk water clearly indicate that a subtle change in the molecular chemistry of the saccharides strongly influences intermembrane interactions and membrane bending rigidities.