A new approach to the data refinement of X-ray reflection measurements from lipid surface monolayers, applied to DMPA on pure water, reveals the structural organization of the lipid in unprecedented detail and provides new insights into headgroup conformation and hydration as a function of lateral pressure. While conventional box models are incapable of modeling the experimental data at high momentum transfer satisfactorily, a quasimolecular composition-space refinement approach using distribution functions to map the spatial organization of submolecular headgroup fragments yields a much better description and overcomes inherent difficulties of box models. Upon going from the fluid liquid-expanded (LE) phase to the hexatic liquid-condensed (LC) phase, the orientation of the headgroup is tightly coupled to the ordering of the acyl chains. Headgroups tilt toward the surface normal to accommodate for the large reduction in available area per lipid molecule. The spread of the headgroup fragment distribution is considerably larger than the global interface roughness and increases slightly with compression. In distinction to earlier work on DMPE using the two-box approach, we find that the phosphate hydration stays essentially constant across the whole isotherm. The discrepancy between the results observed with the different models is attributed to intrinsic deficiencies of the box model.