We present a new data refinement technique for the evaluation of X-ray and neutron reflectometry measurements of interface layers comprising linear molecules. The new method is particularly well-suitedsbut not limited tosmodeling the structure of surface-grafted linear polymers organized in "polymer brushes". In this paper, we discuss technical details of the data inversion technique and demonstrate its capabilities by recovering the structure of a simulated molecular ensemble for which synthetic data sets have been constructed. In the following paper, we utilize this machinery to reveal the nature of a phase transition pertinent to surface-anchored lipopolymers at high molecular densities.