The interface between a ferromagnet (FM) or antiferromagnet (AFM) and a heavy metal (HM) results in an antisymmetric exchange interaction known as the interfacial Dzyaloshinskii-Moriya interaction (iDMI) which favors non-collinear spin configurations. The iDMI is responsible for stabilizing noncollinear spin textures such as skyrmions in materials with bulk inversion symmetry. Interfacial DMI values have been previously determined theoretically and experimentally for FM/HM interfaces, and, in this work, values are calculated for the metallic AFM MnPt and the insulating AFM NiO. The heavy metals considered are W, Re, and Au. The effects of the AFM and HM thicknesses are determined. The iDMI values of the MnPt heterolayers are comparable to those of the common FM materials, and those of NiO are lower.