A systemic formalism is developed that shows how the results for absolute specific volumes of multilamellar lipid dispersions may be combined with results from diffraction studies to obtain quantitative characterizations of the average structure of fully hydrated lipid bilayers. Quantities obtained are the area per molecule, the thickness and volumes of the bilayer, the water layer, the hydrocarbon chain layer and the headgroup layer, and where appropriate, the tilt angle of the hydrocarbon chains. In the case of the C phase of DPPC this formalism leads to the detection of inconsistencies between three data. Results for the G phases of DPPC and DLPE are in reasonable agreement with, though more comprehensive than, previous work that used fewer data and equations. Various diffraction data for the F phase of DPPC are in disagreement and it is shown how this disagreement affects results for the bilayer structure. A recent method of McIntosh and Simon for obtaining fluid phase structure utilizing gel phase structure is slightly modified to obtain results for the F phase of DLPE. Methods of obtaining the average methylene and methyl volumes in the fluid phases are critically examined.