We report on design, fabrication, and magnetooptical studies of a III-V/II-VI hybrid structure containing a GaAs/AlGaAs/ZnSe/ZnCdMnSe double quantum well (QW). The structure design allows one to tune the QW levels into the resonance, thus facilitating penetration of the electron wave function from the diluted magnetic semiconductor ZnCdMnSe QW into the nonmagnetic GaAs QW and vice versa. Magneto-photoluminescence studies demonstrate level anticrossing and strong intermixing resulting in a drastic renormalization of the electron effective g factor, in perfect agreement with the energy level calculations. Comment: 4 pages, 5 Postscript figures, uses revtex4