The authors experimentally demonstrate a resonant hybridization between the magnetic dipole structural resonance in the permeability of a fishnet metamaterial and an electric dipole material resonance in the permittivity of the dielectric spacer layer. The hybrid resonances in the permeability and the negative index response exhibit an anticrossing behavior. A simple analytic model and numerical simulations using a rigorous coupled-wave analysis are in excellent qualitative agreement with the experiment. (C) 2010 American Vacuum Society. [DOI:10.1116/1.3503898]