Lightweight Micro-Perforated Panels (MPP) backed by an air cavity constitute compact sound absorbing resonators, mostly efficient in the mid-frequency range, and that may be constructed using transparent, fibreless and recyclable materials. These soundproof devices have been intensively studied due to their important applications in building acoustics and the aeronautic, astronautic and automotive industries. However, MPPs have been often considered as rigid structures. The work presented here is a theoretical and experimental study on the influence of panel vibrations on the sound absorption and transmission properties of thin MPPs. Measurements show that the absorption performance generates extra absorption peaks or dips that cannot be understood assuming a rigid MPP. A theoretical framework is presented that exactly accounts for structural-acoustic interaction between the MPP and the cavity for general cross-sectional shapes and panel boundary conditions. This model is validated against experimental data acquired from impedance tube, laser vibrometric scans of the panels surface and transmission loss measurements. Coupled-mode analysis explains the nature of the observed spectral peaks for a wide range of perforation ratio and cavity depth.