This paper describes theoretical and experimental investigations into the sound absorption and transmission properties of Micro-Perforated Panels (MPP) backed by an air cavity and a thin plate. A fully-coupled modal approach is proposed to calculate the absorption coefficient and the transmission loss of finite-sized MPP-Cavity-Panel (MPPCP) partitions with conservative boundary conditions. It is validated against infinite partition models and experimental data. A practical methodology is proposed using collocated pressure-velocity sensors to evaluate in an anechoic environment the transmission and absorption properties of conventional MPPCPs. Results show under which conditions edge scattering effects should be accounted for at low frequencies. Coupled mode analysis is also performed and analytical approximations are derived of the resonance frequencies and mode shapes of a flexible MPPCP. It is found that the Helmholtz-type resonance frequency is deduced from the one associated to the rigidly-backed MPPCP absorber shifted up by the mass-air mass resonance of the flexible non-perforated double-panel. Moreover, it is shown analytically and experimentally that the absorption mechanisms at the resonances are governed by a large air-frame relative velocity over the MPP surface, with either in-phase or out-of-phase relationships, depending on the MPPCP parameters.