Temperature dependent experimental Compton profiles of quaternary alloys Co1-x Cu x MnSb (x = 0.0, 0.2, 0.6 and 0.8) when decomposed into constituent profiles show that the sp-electron spin polarization is antiferromagnetically coupled to Mn-3d moments. The orbital magnetic moments derived from combination of magnetic Compton profiles (MCPs) and magnetization measurements are found to be small. Moreover, the first-principles full potential-linearized augmented plane wave (FP-LAPW) calculations have been performed to validate the experimental investigations of spin moments and half-Heusler properties. Present experimental and theoretical work show major role of Mn atoms in building-up the absolute spin moments. Our MCP data and spin-projected density of states derived from FP-LAPW computations show an increase in sp-d interaction in conduction region on increasing the Cu concentration. Further, Ruderman-Kittel-Kasuya-Yosida-type hybridization and antiferromagnetic superexchange interactions are witnessed in the reported alloys.