The solitonic wave processes in a multiferroic structure based on ferroelectric and ferrite layers are studied. The influence of external electric and magnetic fields on frequency and wave-number ranges, where bright and dark solitons can exist, are analysed. The investigation was carried out with the nonlinear Schrodinger equation. Results show that an increase of the electric field shifts the boundary between bright and dark solitons to long-wave region. An increase in magnetic field results in the opposite effect.