Surface plasmon polaritons (SPPs) and standing wave modes provide interesting and exotic properties for infrared metamaterial absorbers. Coupling of these modes promises further development in this field but restricted by the complexity of modes analysis. In this work, we investigate the general phenomenon of modes coupling supported by a metal (with grating)-dielectric-metal sandwich structure based on rigorous coupled-wave analysis (RCWA) method and experiment results. Through the analysis of fundamental modes, a new approach based on the boundary conditions is introduced to reveal the coupling mechanism and the corresponding resonance shifting phenomenon with simple but rigorous derivations. The strong coupling between SPPs excited on the dielectric-metal interfaces and rigorous modes of standing waves in the dielectric layer can be manipulated to improve the detection sensitivity of sensors and emissivity efficiency of infrared emitters.