The effect of the bandgap width between the first and second energy minibands on the charge transport in a semiconducting superlattice to which electric and tilted magnetic fields are applied is studied theoretically. The time dependences of the current passing through the superlattice are calculated, and the dependences of the amplitude and frequency of electric current oscillations on the applied voltage are constructed. It is found that the interminiband electron tunneling facilitates a decrease in the amplitude of current oscillations, but simultaneously increases their frequency.