Statistical modal Energy distribution Analysis (SmEdA) may be used as alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of the sound transmission through a thin light structure, it is well-known than the non-resonant response of the structure may have a significant role on the transmission below the critical frequency. In this paper, one presents an extension of SmEdA taking into account the contributions of the non resonant modes of the thin structure. The dual modal formulation (DMF) is used for describing the behavior of two acoustic cavities separated by a thin structure knowing their subsystem modes. A condensation in the DMF equations is achieved on the amplitudes of the non-resonant modes. Using some simplifications, a new coupling scheme between the resonant modes of the three subsystems is obtained. It shows direct couplings of the cavity modes through stiffness elements characterized by the modes shapes of the cavities and the structure, both. Comparisons with reference results show the ability and the interest of the present approach for representing the nonresonant contributions of the structure.