We report magnetic and magnetoresistance (MR) measurements in the current-in-plane (CIP) and current-perpendicular-to-the-plane (CPP) geometries of multilayers and spin-valve structures based on the predicted half-metallic (100% spin-polarized) ferromagnetic Heusler alloy NiMnSb. Multilayers of the form [NiMnSb/Cu]X10, as well as a trilayer spin valve of the form [NiMnSb/Cu/Y] (Y=Ni80Fe20 and NiMnSb/FeMn) have been grown using a low-rate, low-pressure sputtering deposition technique. The multilayers do not show evidence of antiferromagnetic coupling between the NiMnSb layers, and the measured CPP magnetoresistance is 4.5% at 4.2 K. NiMnSb/Cu/NiFe spin valves and NiMnSb/Cu/NiMnSb/FeMn quasispin-valves adopt more closely antiparallel alignments of adjacent magnetic layer magnetizations, and CPP MR ratios as high as 7.2% are measured at 4.2 K. Although these CPP MRs are larger than the CIP MRs for similar samples, the largest CPP MR observed is still smaller than expected for a 100% spin-polarized material.