The enhanced middle-infrared light transmission through Au/SiO(x)N(y)/Au aperture arrays by changing the refractive index and the thickness of a dielectric layer was studied experimentally. The results indicated that the transmission spectra was highly dependent on the refractive index and the thickness of SiO(x)N(y). We found that the transmission peaks redshifted regularly along with the refractive index from 1.6 to 1.8, owing to the role of surface plasmon polaritons (SPP) coupling in the Au/SiO(x)N(y)/Au cascaded metallic structure. Simultaneously, a higher transmission efficiency and narrower transmission peak was obtained in Au/SiO2.1N0.3/Au cascaded metallic structure with small refractive index (1.6) than in Au/SiO0.6N1/Au cascaded metallic structure with large refractive index (1.8). When the thickness of SiO(x)N(y) changes from 0.2 to 0.4 microm, the shape of transmission spectra exhibits a large change. It was found that a higher transmission efficiency and narrower transmission peak was obtained in Au/SiO(x)N(y)/Au cascaded metallic structure with a thin dielectric film (0.2 microm), with the increase of SiO(x)N(y) film's thickness, the transmission peak gradually widened and disappeared finally. This effect is useful in applications of biochemical sensing and tunable integrated plasmonic devices in the middle-infrared region.