To better exert the vibration suppression effect of magnetorheological elastomer (MRE) embedded into a composite structure with structural and functional integration advantage, this study proposes a nonlinear analytical model of such composite plate with an MRE function (MREF) layer, accounting for internal magnetic and temperature fields for the first time. Initially, a 9-layer fiber metal laminated (FML) plate with the MREF composites, consisting of two layers of metal protective skins, two layers of fiber-reinforced polymer (FRP) and one layer of MREF, is taken as an example to describe such a modelling method. Nonlinear expressions of elastic moduli of MRE and FRP involving thermal and magnetic fitting coefficients are also proposed, followed by derivation of the energy expressions of the constituent layers by the Rayleigh-Ritz method. After the free and forced vibrations are solved, the identification procedure of fitting coefficients is described and some literature results are employed to preliminarily validate this model without consideration of internal magnetic field or temperature field or both. Finally, dynamic experiments under different magnetic and temperature conditions are undertaken. The detailed comparison of the natural frequencies and resonant responses are conducted to provide a solid validation of the model developed. It has been found that enlarging the magnetic and temperature fields both facilitate the improvement of the anti-vibration performance. Also, by further increasing the shear modulus of MRE, the volume fraction of carbonyl iron particles or the thickness ratio of the MRE layer to the overall structure, a better vibration suppression capability can be obtained.