Magnetoelectric composite nanoparticles of BaTiO3:CoFe2O4 have been synthesized and characterized. Microstructure analysis and electromagnetic behaviour of the spinel core (cobalt ferrite) and perovskites shell (barium titanate) of the core-shell magnetoelectric nanoparticles using transmission electron microscopy, off-axis electron holography and piezo-response force microscopy has been investigated. The result shows the coating layer of BaTiO3 is highly uniform in composition and thickness around the core. Such a uniform deposition of perovskites on spinel with expected high lattice mismatch is unique. Also, the optoacoustic measurements and MENR-cellular interactions proves the magnetoelectricity behaviour of the nanostructure via stress transfer from core to shell in the presence of applied magnetic field. The results are discussed in details.