Specular and off-specular neutron scattering are used to study the influence of molecular chemistry (mutation) on the intermembrane interactions and mechanical properties of the outer membrane of Gram-negative bacteria consisting of lipopolysaccharides (LPSs). For this purpose, solid-supported multilayers of mutant LPS membranes are deposited on silicon wafers and hydrated either at defined humidity or in bulk buffers. The planar sample geometry allows to identify out-of-plane and in-plane scattering vector components. The measured two-dimensional reciprocal space maps are simulated with membrane displacement correlation functions determined by two mechanical parameters (vertical compression modulus and bending rigidity) and an effective cutoff radius for the membrane fluctuation wavelength. Experiments at controlled humidity enable one to examine the influence of the disjoining pressure on the saccharide-mediated intermembrane interactions, while experiments in bulk buffers (i.e., in the absence of an external osmotic stress) reveal the effect of divalent cations on LPS membranes, highlighting the role of divalent cations in the survival mechanism of bacteria in the presence of antimicrobial molecules.