The phase behavior of a supported dimyristoylphosphatidylcholine (DMPC) bilayer system has been investigated using neutron reflectivity. The bilayer is fabricated by a combination of Langmuir-Blodgett, Langmuir-Schaeffer, and self-assembly techniques, and while robustly associated with the substrate, the bilayer remains separated from it by a substantial layer of water, due to a Helfrich type entropic repulsion. The reflectivity data have been analyzed using a quasi-molecular model, similar to that used by Wiener and White (Wiener et al. Biophys. J. 1992, 61, 434-447) allowing easy comparison of the bilayer structure with other systems such as vesicles. The area per molecule (APM) and bilayer thickness in the gel phase are found to be identical to those in DMPC vesicles. In going from the gel phase to the fluid phase, the bilayer thickness decreases and the APM increases due to chain melting. This suggests that the bilayer is minimally constrained, since the bilayer structure seems to be determined by the packing requirements of the phospholipids rather than any influence of the substrate. The hydrating layer is thicker than in vesicles, and we suggest that this may be due to differences in the confinement regime. That is, a bilayer in a multilamellar vesicle is constrained on both sides, whereas the bilayer studied here is confined on one side only. Nevertheless, the thickness of the intervening water layer decreases across the main transition in the same way as is seen in multilamellar systems.