Investigations of the hydration repulsion between hydrophilic soft interfaces in water, in particular between lipid membranes, rely on accurate experimental measurements of the associated pressure-distance curves. Conventional experimental approaches face challenges especially when it comes to the pressure-distance curves between dissimilar surfaces, a scenario with particular value for the study of the mechanisms responsible for the hydration repulsion. Here, we present an alternative approach based on solid-supported inverse lipid bilayers (ILBs) in which two hydrophilic monolayer surfaces face each other across a thin water layer, as evidenced through x-ray reflectometry. The water uptake as a function of the dehydrating osmotic pressure is precisely measured with the help of ellipsometry under controlled humidity conditions. The measurements reproduce the known hydration decay lengths of interacting phospholipid membrane surfaces and of interacting glycolipid membrane surfaces. In addition, we present pressure-distance curves of the interaction between two dissimilar membrane surfaces, with phospholipids on one side and glycolipids on the other side. These unique measurements of asymmetrical interaction scenarios result in a curve that is very similar to that of two interacting glycolipid membrane surfaces, which can be rationalized on the basis of our current knowledge of the repulsion mechanisms.