Layered magneto-electro-elastic (MEE) composites with imperfect interface have been investigated in recent years for enhancing the important magnetoelectric coupling effect. However, the impact of the imperfect interface on the elastic, electric and magnetic behaviors has not been studied in details so far. In this paper, a simply supported and multilayered MEE plate with one of the typical imperfect interfaces is proposed to deeply understand the response of the layered plate under surface loading, which mimics the simple tests used in experiments. Based on the extended pseud Stroh formalism and the dual variable and position method, the analytical solutions for anisotropic and multilayered MEE plates with imperfect interfaces are derived. In our numerical studies, we choose BaTiO3 (BTO) as the piezoelectric phase and CoFe2O4 (CFO) as the piezomagnetic phase to construct two sandwich plates (BTO/CFO/BTO, and CFO/BTO/CFO). Under surface loading, responses of these two sandwich plates are analyzed which demonstrate the possibility of optimal tuning the elastic, electric and magnetic fields.