A double-layer metal film grating with a composite periodic structure is designed, which features multiple frequency bands, multi-characteristic integration. The simulation by a finite element method, and we find that this structure can achieve high absorption at resonant wavelengths of 760, 904, 1028, and 1216 nm under transverse-magnetic (TM) polarized illumination on the bottom of the nanograting at an incident angle of 65°. Its absorptivity can be up to 98.73%, 92.84%, 97.57%, and 99.11%, respectively. Further simulation reveals that multiband absorption peaks also possess the characteristics of narrowband polarization filtering and refractive index sensing. Its maximum refractive index sensitivity is 2080 nm/RIU and the maximum figure of merit (FOM) is 92.1 RIU ^-1. In addition, period modulation enables the tunability of narrowband polarization filtering in a wide near-infrared wavelength range from 944 nm to 1206 nm. We explore the underlying integration mechanism by analyzing the distributions of the surface electromagnetic field, surface current, and surface electric charges. The results show that the designed double-layer metal film grating with a composite periodic structure has a broad application perspective in miniaturized and highly integrated multispectral infrared detection, spectral imaging, and biosensing.