Multilayer films consisting of ferromagnetic PtMnSb and antiferromagnetic CuMnSb were prepared by a dual-type rf sputtering method. The thickness of a PtMnSb layer (dPt) was designed from 3.6 ?? to 100 ??, holding the CuMnSb layer thickness constant at 100 ??. From X-ray diffraction data, all multilayer films were found to have a [111] texture of the C1b-type Heusler structure. The magnetization of multilayer films showed anomalous behavior: 1) a great enhancement of the magnetization compared with that of a PtMnSb compound; and 2) a bend in the temperature dependence of the magnetization at about 50 K, near the Neel temperature of CuMnSb. The magnetization curve revealed that a perpendicular magnetic anisotropy was induced with decreasing dPt. The interface contribution (Ks) and the volume contribution (Kv) to the perpendicular magnetic anisotropy were estimated to be Ks = 0.14 erg/cm2 and Kv = ??7.9 ?? 106 erg/cm3.