A novel experimental setup has been used to measure the specularly-reflected neutron intensity from a model biological membrane containing components from the outer membrane of Neurospora crassa mitochondria. The specular reflectivity from a single bilayer membrane, formed by the fusion of vesicles onto a phospholipid monolayer supported on a flat substrate, was measured in both D2O and H2O solvents. In D2O solvent, reflected neutron intensities down to 10(-6) were measured for wavevector transfers out to 0.25 Angstrom(-1). A symmetric model for the neutron scattering length density profile perpendicular to the bilayer surface was constructed based on fits to the D2O data. The overall bilayer thickness was found to be 43 +/- 2 Angstrom. The individual lipid head group and hydrocarbon tail layer thicknesses were 7.5 +/- 1.4 and 28.0 +/- 2.8 Angstrom, respectively. The fitted results are consistent with the H2O data. The integrity of the model membrane bilayer was confirmed by comparing its measured reflectivity to that obtained from a single lipid bilayer consisting of soybean phospholipids (asolectin) which was deposited on a flat substrate by the Langmuir-Blodgett technique.