A new interpretation of neutron reflectivity data for surfactants adsorbed on hydrophilic solid surfaces has been developed. Motivated by recent atomic force microscopy results, a model of the adsorbed layer is constructed based upon an adsorbed layer consisting of discrete, micelle-like surfactant aggregates of well-defined geometries. Scattering length density profiles and reflectivity curves are calculated for conventional, laterally unstructured adsorbed layers (a bilayer), as well as for cylindrical and spherical surfactant aggregates adsorbed on a hydrophilic surface. It is shown that treating such structured surfactant films as bilayers often results in a good fit to neutron reflectivity data, but that fit parameters lead one to underestimate the film thickness and overestimate the fractional surface coverage by the adsorbed film.