Dual-layer metallic wire-hole structures were fabricated and their terahertz transmission properties were measured. They exhibit polarization-dependent transmittance with large extinction ratios. Simulation and experimental results on structures with different wire-to-hole orientations provide strong evidence that the resonance peaks are caused by plasmonic coupling between the two metallic layers. A simplified LC-circuit model is proposed to explain the coupling mechanism and to estimate the peak frequencies. Our results suggest that specific electromagnetic response can be achieved by appropriate design of the geometrical patterns on the two metallic layers and a suitable polarization of the incident wave.