Global maps of hydrogen abundance near the surface of Mars, interpreted as the mass percent of water-equivalent hydrogen (WEH) have been generated from measurements of neutron leakage fluxes from Mars. Although these data provide an unambiguous indicator of the presence of WEH, quantitative details of its magnitude and burial depth depend on the model of the host regolith that is used to interpret the data. Previous models assumed a spatially uniform surface cover layer having a one-to-two mass percent of WEH and thickness D covering a semi-infinite ice-rich deposit. These assumptions allowed the derivation of the relative proportions of ice and regolith in the lower layer, which had been used to create global maps of WEH in the near surface. In this paper we develop a new method that determines, from the Mars Odyssey Neutron Spectrometer (MONS) data, a self-consistent model of the WEH content of both the upper and lower layers as well as the thickness (D) of the upper layer. The results of our model suggest that large areas at nonpolar latitudes may contain water ice deposits that have abundances that are larger than can be held by normal pore volumes. These deposits are buried less than about 1 m below the surface and may represent buried water ice or high concentrations of hydrous minerals. Intriguingly, the most definitive MONS evidence at intermediate latitudes for excess ground ice corresponds to a region of Arcadia Planitia within which High Resolution Imaging Science Experiment (HiRISE) has observed fresh icy craters.