A study on magnetoelectric phenomena in the barium titanate-barium hexaferrite (BaTiO3-BaFe12O19) composite system, using high resolution techniques including switching spectroscopy piezoresponse force microscopy (SSPFM) and spatially resolved confocal Raman microscopy (CRM), is presented. It is found that both the local piezoelectric coefficient and polarization switching parameters change on the application of an external magnetic field. The latter effect is rationalized by the influence of magnetostrictive stress on the domain dynamics. Processing of the Raman spectral data using principal component analysis (PCA) and self-modelling curve resolution (SMCR) allowed us to achieve high resolution phase distribution maps along with separation of average and localized spectral components. A significant effect of the magnetic field on the Raman spectra of the BaTiO3 phase has been revealed. The observed changes are comparable with the classical pressure dependent studies on BaTiO3, confirming the strain mediated character of the magnetoelectric coupling in the studied composites.