The continuous evolution toward electronics with high power densities and integrated circuits with smaller feature sizes and faster speeds places high demands on a set of material properties, namely, the electrical, thermal, and mechanical properties of polymer dielectrics. Herein, a supramolecular approach is described to self-healable polymer nanocomposites that are mechanically robust and capable of restoring simultaneously structural, electrical, dielectric, and thermal transport properties after multiple fractures. With the incorporation of surface-functionalized boron nitride nanosheets, the polymer nanocomposites exhibit many desirable features as dielectric materials such as higher breakdown strength, larger electrical resistivity, improved thermal conductivity, greater mechanical strength, and much stabilized dielectric properties when compared to the pristine polymer. It is found that the recovery condition has remained the same during sequential cycles of cutting and healing, therefore suggesting no aging of the polymer nanocomposites with mechanical breakdown. Moreover, moisture has a minimal effect on the healing and dielectric properties of the polymer nanocomposites, which is in stark contrast to what is typically observed in the hydrogen-bonded supramolecular structures.