The acoustic transmittance of a pair of closely-spaced plates, each perforated with a square array of subwavelength diameter holes, an “acoustic double fishnet” structure, is explored. For frequencies below onset of diffraction, there is a band of near-perfect acoustic attenuation at a frequency dictated by the periodicity of the array.  Comparison of experimental data with analytical modeling shows that the observed response is due to a hybridization between pipe modes within the holes and the two dimensional resonance supported in the gap between the periodically perforated plates.