(001)-oriented Ni80 Fe20 Mn100-x Ptx and Co90 Fe10 Mn100-x Ptx epitaxial bilayers were prepared using the molecular beam epitaxy method. Their exchange anisotropies were measured using a torque magnetometer, while their interfacial Mn uncompensated moments were measured by means of x-ray magnetic circular dichroism. The bilayers exhibited both one- and fourfold components in their anisotropy torque curves, which are difficult to explain using a simple model assuming the coherent rotation of ferromagnetic (F) and antiferromagnetic (AF) spins. Uncompensated Mn moments were confirmed to exist in the Mn100-x Ptx layer due to exchange coupling with the adjacent F layer, and the Mn moment of CoFe Mn100-x Ptx was found to be larger than that of NiFe Mn100-x Ptx. In order to understand the experimental results, we extended the Mauri [J. Appl. Phys. 62, 3047 (1987)] domain wall model by assuming cubic anisotropy in the AF and four AF domains whose interfacial moments are oriented along the principal axis of (001)-oriented Mn-Pt. The model predicted the uncompensated AF moment resulting from the domain wall formed in the AF layer and well reproduced the coexistence of one- and fourfold anisotropies in the in-plane torque curves. The uncompensated moment and torque curve were found to be dependent on the ratio of F/AF interfacial exchange coupling and the AF domain wall energy. By changing the ratio, it was possible to reproduce exchange anisotropy for various systems, such as NiFeMnPt, NiFeMnIr, and CoFeMnPt.