Using the space-resolved Brillouin light scattering spectroscopy we study the transformation of dynamic magnetization patterns in a bilayer multiferroic structure. We show that in the comparison with a single yttrium iron garnet (YIG) film magnetization distribution is transformed in the bilayer structure due to the coupling of waves propagating both in an YIG film (magnetic layer) and in a barium strontium titanate slab (ferroelectric layer). We present a simple electrodynamic model using the numerical finite element method to show the transformation of eigenmode spectrum of confined multiferroic. In particular, we demonstrate that the control over the dynamic magnetization and the transformation of spatial profiles of transverse modes in magnetic film of the bilayer structure can be performed by the tuning of the wavevectors of transverse modes. The studied confined multiferroic stripe can be utilized for fabrication of integrated dual tunable functional devices for magnonic applications.