This paper presents further analysis of a system containing two graphene plates with attached phosphatidylcholine lipid headgroups embedded in water, which models a lipid bilayer. Previously, we performed molecular dynamics simulations on this System, Calculated the potential of mean force (PMF) between plates (Eun, C.; Berkowitz, M. L. J. Phys. Chem. B 2009, 113, 13222-13228), and also performed a Structural analysis of water in the confined space between the plates. Here, we perform thermodynamic analysis of the PMF and, in addition to the previous analysis of water that considered density plots and the OH bond orientational profiles, we perform hydrogen bonding analysis of water. We show that the structural analysis of water is consistent with the thermodynamic results we obtained for the PMF.