Multiple absorption bands in a metal-insulator-metal (MIM) nanostructure are comprehensively investigated in the visible and near-infrared (near-IR) regime. The MIM nanostructure consists of patterned gold squares with systematically varying size and period atop a thin aluminum nitride dielectric layer on a thick gold film. Both the transverse-electric (TE) slab-waveguide mode and the transverse-magnetic (TM) surface plasmon-polariton mode can be excited in the nanostructure. Grating coupling of the incident light into nonlocalized traveling waves is found from electromagnetic field patterns and from the linear dispersion of the absorption modes with period. A localized mode strengthens the near-IR absorption band for small square sizes, and the resonance shifts to red for large square sizes.