In this study, thermoplastic elastomer nanocomposites based on linear low density polyethylene (LLDPE)/silicone rubber (SR; 90:10) filled with a 2 vol% boron nitride (BN) nanofiller were exposed to electron beam (EB) irradiation at low irradiation doses (20, 40, 50, and 100 kGy). The response of the LLDPE/SR/BN nanocomposites to the EB irradiation crosslinking was examined and compared with the non‐irradiated samples in terms of dielectric properties (permittivity and loss tangent), dielectric breakdown strength, morphology, and rheological properties. A swelling study was performed to quantify the degree of crosslinking and it was found that the crosslink density increased slightly upon EB irradiation. Scanning electron microscopy results provided evidence that the SR phase was selectively crosslinked and interfacial adhesion was improved in irradiated samples. A good correlation was observed between the morphology and the dynamic storage modulus obtained from the melt rheological experiments. The optimum irradiation dose was found to be 20 kGy, which was marked by an improved dielectric breakdown strength, a permittivity‐frequency curve plateau and a reduced loss tangent value. POLYM. ENG. SCI., 58:E135–E144, 2018. © 2017 Society of Plastics Engineers