A matrix method for evaluating effective electro-magneto-thermo-elastic properties of a generally anisotropic multilayered composite is presented. Physical variables are categorized into two groups: one that satisfies the continuity across the interface between layers and another that satisfies an average inter-layer compatibility (which is also exact). The coupled electro-magneto-thermo-elastic constitutive equation is accordingly reassembled into submatrices, which leads to the derivation of concise and exact matrix expressions for effective properties of a multilayered composite having the coupled physical effects. Comparing the results for a purely elastic multiplayer with those from other theoretical approaches validates the developed method. Examples are given for a PZT-graphite/epoxy composite and a $BaTiO_3-CoFe_2O_4$ multiplayer which exhibit piezo-thermoelastic and magnetoelectric properties, respectively. The result shows how a strong magnetoelectric effect can be achieved by combining piezoelectric and piezomagnetic materials in a multilayered structure. The magnetoelectric coefficient of the $BaTiO_3-CoFe_2O_4$ multiplayer is compared with those for fibrous and particulate composites fabricated with the same constituents.