The electronic band-edge spectrum of the interface states in the magnetic semiconductor quantum wells based on narrow-gap semiconductors with mutually inverted band arrangement is studied within the envelope-function formalism. Interface states are shown to appear in these structures in the case of overlapping bulk bands of the constituents. The hybridization between the bare sp-electron states and the d states of the Mn atoms leads to spin splitting. The spin-splitting effect of the interface states as a function of external magnetic field, well width, band offsets, and fraction of the magnetic atoms, is studied. One essential result is that one can design a structure where the states localized at the interfaces only have one spin direction. The results give evidence of the perspective for using the magnetic semiconductor structures in spin electronics.