We study the electronic and magnetic properties of the interfaces between the half-metallic Heusler alloy NiMnSb and the binary semiconductors InP and GaAs using two different state-of-the-art full-potential ab initio electronic structure methods. Although in the case of most NiMnSb/InP(001) contacts the half-metallicity is lost, it is possible to keep a high degree of spin polarization when the interface is made up by Ni and P layers. In the case of the GaAs semiconductor, the larger hybridization between the Ni-d and As-p orbitals with respect to the hybridization between the Ni-d and P-p orbitals destroys this polarization. The (111) interfaces present strong interface states, but also in this case there are few interfaces presenting a high spin polarization at the Fermi level which can reach values up to 74%.