Neutron reflectivity experiments have been performed to investigate the adsorption behavior of aqueous solutions of n-2-butoxyethanol (n-C4E1) and i-2-butoxyethanol (i-C4E1) in D2O against a hydrophilic silica substrate. The measurements were made in the one-phase region near the lower critical solution point of the aqueous systems. At temperatures removed from the lower critical solution temperature, T-LCS, evidence for the existence of a microscopically thick (similar to40 Angstrom) adsorbed D2O-rich layer is presented along with data suggesting that the amphiphile is strongly depleted from the boundary layer. Experiments using a thick "tuning" layer of silica reinforce these observations. Analysis of the data as T-->T-LCS reveals that the region beneath the adsorbed D2O-rich layer becomes increasingly enriched with D2O, and the nature of the composition profile normal to the interface has been considered. Analysis identifies the exponent describing the power-law decay part of the critical adsorption profile appended to the D2O-rich region and associates a temperature-dependent correlation length with the critical adsorption profile. Ellipsometric data are presented which complement the neutron reflectivity results. The adsorption behavior of the n-C4E1 and i-C4E1 systems are found to be very similar with the only discernible difference being the magnitude of the adsorption preference of water for the n-C4E1 system in the long-range profile.