Multilayer superlattices consisting of multiferroic Bi(2)NiMnO(6) (BNMO) and La(2)NiMnO(6) (LNMO) have been grown heteroepitaxially on pure and Nb-doped SrTiO(3) substrates using the pulsed laser deposition technique. In a series of superlattice structures grown with a fixed BNMO layer thickness of ten unit cells, we find that the c-axis lattice parameter, Curie temperature and magnetocapacitance are strongly dependent upon the number of stacked LNMO unit cells in the repeating units. The thickness-dependent magnetodielectric effect is attributed to the fluctuations in electric and magnetic dipole ordering due to the substrate and interface induced stress in the superlattice structures. An enhanced magnetodielectric effect in multilayers with LNMO thicknesses larger than six unit cells is explained based on possible canting of spin at the interfaces of LNMO and BNMO.