Langmuir monolayers provide an important system for the investigation of the intramolecular structure and intermolecular ordering of organic and bio-organic macromolecular amphiphiles at an interface between polar and nonpolar media, e.g., the liquid-gas interface. Specular x-ray and neutron reflectivity have contributed substantially to these investigations. However, these reflectivity techniques are generally limited by the absence of crucial phase information, the relatively small contribution of the amphiphile to the scattering-length density contrast across the interface, and the relatively limited range of momentum transfer available perpendicular to the interface. Although several procedures have been developed to provide model-independent solutions to the phase problem, there remains a limited ability to distinguish features of slightly differing contrast (i.e., the "sensitivity") as well as their minimum allowable separation (i.e., the "spatial resolution") along the length of the scattering-length density profile derived from the reflectivity data via solution to the phase problem. Here, we demonstrate how the well-known interferometric approach can be extended to the structural investigation of otherwise unperturbed Langmuir monolayers of these amphiphiles to provide a direct solution to the phase problem and importantly, substantially enhance both the sensitivity and the spatial resolution in the derived profiles.