Using 237 all-atom double bilayer simulations, we examined the thermodynamic and structural changes that occur as a phosphatidylcholine lipid bilayer stack is dehydrated. The simulated system represents a micropatch of lipid multilayer systems that are studied experimentally using surface force apparatus, atomic force microscopy and osmotic pressure studies. In these experiments, the hydration level of the system is varied, changing the separation between the bilayers, in order to understand the forces that the bilayers feel as they are brought together. These studies have found a curious, strongly repulsive force when the bilayers are very close to each other, which has been termed the "hydration force," though the origins of this force are not clearly understood. We computationally reproduce this repulsive, relatively free energy change as bilayers come together and make qualitative conclusions as to the enthalpic and entropic origins of the free energy change. This analysis is supported by data showing structural changes in the waters, lipids and salts that have also been seen in experimental work. Increases in solvent ordering as the bilayers are dehydrated are found to be essential in causing the repulsion as the bilayers come together.