Earlier works on the retrieval of 3-D bounded dielectric and/or magnetic inclusions buried in free space are extended to the demanding case of inclusions in a half space. Starting from the exact contrast-source vector integral formulations satisfied by the time-harmonic fields, and using proper reciprocity relationships of the dyadic Green's functions, asymptotic field formulations are proposed, the leading orders of which yield the MultiStatic Response matrix of the collection. Its singular value decomposition in particular leads to a MUSIC cost functional the 3-D map of which peaks at the locations of the inclusions. Numerical results from synthetic data are given.