Neutron reflectivity has allowed the measurement at nanometric resolution of the structures formed when high internal phase water/oil emulsions are in contact with hydrophobic and hydrophilic surfaces prepared at planar faces of silicon blocks. The emulsion was a dispersion of micrometer sized droplets of saltwater-in-hexadecane. Contrast variation by selective deuteration of different components of the emulsion shows that at nanometric resolution an oil-rich phase is produced at the solid-emulsion interface independent of the nature of the solid surface. There is an almost complete surfactant monolayer at the hydrophilic solid face and then a hexadecane-rich layer that persists for 150 Angstrom. Both are less pronounced for the hydrophobic surface, but not qualitatively different. The hexadecane-aqueous interfaces are highly curved with an similar to500 Angstrom radius-compared with the micron radius of the aqueous droplets.