We examine the ballistic conduction through Au-NiMnSb-Au heterostructures consisting of up to four units of the half-metallic NiMnSb in the scattering region, using density functional theory (DFT) methods. For a single NiMnSb unit the transmission function displays a spin polarization of around 50% in a window of 1eV centered around the Fermi level. By increasing the number of layers, an almost complete spin polarization of the transmission is obtained in this energy range. Supplementing the DFT calculations with local electronic interactions, of Hubbard-type on the Mn sites, leads to a hybridization between the interface and many-body states. The significant reduction of the spin polarization seen in the density of states is not apparent in the spin polarization of the conduction electron transmission, which suggests that the hybridized interface and many-body induced states are localized.