The manipulation of the magnetization by spin-orbit torques (SOTs) has recently been extensively studied due to its potential for efficiently writing information in magnetic memories. Particular attention is paid to non-centrosymmetric systems with space inversion asymmetry, where SOTs emerge even in single-layer materials. The half-metallic half-Heusler PtMnSb is an interesting candidate for studies of this intrinsic SOT. Here, we report on the growth and epitaxial properties of PtMnSb thin films and PtMnSb/Pt bilayers deposited on MgO(001) substrates by dc magnetron co-sputtering at high temperature in ultra-high vacuum. The film properties were investigated by x-ray diffraction, x-ray reflectivity, atomic force microscopy, and electron microscopy. Thin PtMnSb films present a monocrystalline C1b phase with (001) orientation, coexisting at increasing thickness with a polycrystalline phase with (111) texture. Films thinner than about 5 nm grow in islands, whereas thicker films grow layer-by-layer, forming a perfect MgO/PtMnSb interface. The thin PtMnSb/Pt bilayers also show island growth and a defective transition zone, while thicker films grow layer-by-layer and Pt grows epitaxially on the half-Heusler compound without significant interdiffusion.