Triple points on direct-bond copper substrates for packaging medium-voltage power modules are locations of high electric-field stress responsible for partial discharge in the encapsulation material. In this work, a nonlinear resistive polymer-nanoparticle composite was tested for coating the triple points to reduce the electric-field intensity. This approach of field grading avoided using thick layers of insulation, thus improving the thermal performance of the module. The field-grading effect was first analyzed by COMSOL field simulations. The maximum electric-field intensity at the triple points of a coated alumina direct-bond-copper substrate was reduced by up to 43%. This field reduction was verified from a measured increase of 86% in the partial discharge inception voltages of coated over uncoated substrates encapsulated in a silicone gel. Coated substrates with 1-mm thick alumina and 3-mm trench gap were found to have no partial discharge higher than 10 pC under 19 kV for 5 minutes, leaving a significant insulation margin for packaging 15-kV silicon carbide power devices. Given its processing simplicity and effective field-stress reduction, the nonlinear resistive composite offers a low-cost solution for packaging medium-voltage power devices without compromising the package thermal performance.