This paper deals with the acoustics of rigid porous media with inner resonators both saturated by the same gas. The aim is to define porous media microstructures in which inner resonance phenomena may occur, and to provide the modeling of acoustic waves in this situation. The first part, focuses on the design of a periodic medium consisting in damped Helmholtz resonators embedded in a porous matrix. In the second part, the macroscopic description of this system is established through the homogenization method. In the third part, the features of acoustic wave propagation are determined, and the occurrence of a broad band gap along with strongly dispersed waves is discussed according to the characteristics of the porous matrix and of the damped resonators.