Electromagnetic bandgap (EBG) structures in a pair of parallel planes are quite effective for suppressing simultaneous switching noise, but they are too large to be applied to compact electronic devices. To miniaturize the EBG structures, we investigated an approach to interpose a high-permeability magnetic metal sheet between the parallel planes. The experimental results show that high permeability of the sheet shifts the stopband towards lower frequencies. This suggests that such sheets contribute to the miniaturization of the EBG structures. In addition, it is demonstrated that the imaginary part of the permeability can expand the stopband.