Theoretical and experimental results are presented into the sound absorption and transmission properties of multi-layer structures made up of thin micro-perforated panels (ML-MPPs). The objective is to improve both the absorption and insulation performances of ML-MPPs through impedance boundary optimization. A fully coupled modal formulation is introduced that predicts the effect of the structural resonances onto the normal incidence absorption coefficient and transmission loss of ML-MPPs. This model is assessed against standing wave tube measurements and simulations based on impedance translation method for two double-layer MPP configurations of relevance in building acoustics and aeronautics. Optimal impedance relationships are proposed that ensure simultaneous maximization of both the absorption and the transmission loss under normal incidence. Exhaustive optimization of the double-layer MPPs is performed to assess the absorption and/or transmission performances with respect to the impedance criterion. It is investigated how the panel volumetric resonances modify the excess dissipation that can be achieved from non-modal optimization of ML-MPPs.