Lipopolysaccharides (LPSs) are a major class of macromolecules populating the surface of Gram-negative bacteria. They contribute significantly to the bacterium's surface properties and play a crucial role in regulating the permeability of its outer membrane. Here, we report on neutron diffraction studies performed on aligned, self-assembled bilayers of LPS isolated from Pseudomonas aeruginosa PAO1. This LPS system is comprised of a mixture of rough and smooth A-band and B-band LPS, similar to that naturally found in P. aeruginosa. Temperature scans were conducted at various levels of hydration, and the phases adopted by LPS, along with their corresponding transition temperatures, have been identified. Because of LPS's chemical heterogeneity, the gel-to-liquid-crystalline transition was continuous and not abrupt as commonly observed in single-component phospholipid systems. From the construction of one-dimensional scattering length density profiles, we find that water penetrates into the hydrocarbon region up to and including the center of liquid-crystalline LPS bilayers. This permeability to water also extends to bilayers in the continuous phase transition region and could have far-reaching implications as to how small molecules penetrate the outer membrane of Gram-negative bacteria.