Thin films of multiferroic Bi2NiMnO6 (BNMO) have been epitaxially stabilized on various lattice-matched substrates using the pulsed laser deposition technique. BNMO films deposited on conducting Nb doped SrTiO3 substrates exhibit a magnetodielectric effect, in which the effective dielectric constant is dependent on the applied magnetic field and measurement frequency. A rapid change in the effective dielectric constant with a corresponding maximum in the magnetodielectric effect is observed near the ferromagnetic transition temperature of BNMO. The temperature-dependent magnetodielectric effect is attributed to the coupling between electric dipole ordering and fluctuations and magnetic ordering and fluctuations.