We present experiments and analysis on enhanced transmission due to dielectric layer deposited on a metal film perforated with two-dimensional periodic array of subwavelength holes. The Si3N4 overlayer is applied on the perforated gold film (PGF) fabricated on GaAs substrate in order to boost the transmission of light at the surface plasmon polariton (SPP) resonance wavelengths in the mid- and long-wave IR regions, which is used as the antireflection (AR) coating layer between two dissimilar media (air and PGF/GaAs). It is experimentally shown that the transmission through the perforated gold film with 1.8 µm (2.0 µm) pitch at the first-order (second-order) SPP resonance wavelengths can be increased up to 83% (110%) by using a 750 nm (550 nm) thick Si3N4 layer. The SPP resonance leads to a dispersive resonant effective permeability (μeff ≠ 1) and thereby the refractive index matching condition for the conventional AR coating on the surface of a dielectric material cannot be applied to the resonant PGF structure. We develop and demonstrate the concept of AR condition based on the effective parameters of PGF. In addition, the maximum transmission (zero reflection) condition is analyzed numerically by using a three-layer model and a transfer matrix method is employed to determine the total reflection and transmission. The numerically calculated total reflection agrees very well with the reflection obtained by 3D full electromagnetic simulations of the entire structure. Destructive interference conditions for amplitude and phase to get zero reflection are well satisfied.