  The proximity effect in a model manganite-cuprate system is investigated
theoretically. We consider a situation in which spin-polarized electrons in
manganite layers antiferromagnetically couple with electrons in cuprate layers
as observed experimentally. The effect of the interfacial magnetic coupling is
found to be much stronger than the injection of spin-polarized electrons into
the cuprate region. As a result, the superconducting transition temperature
depends on the thickness of the cuprate layer significantly. Since the magnetic
coupling creates {\em negative} spin polarization, an applied magnetic field
and the negative polarization compete resulting in the inverse spin-switch
behavior where the superconducting transition temperature is increased by
applying a magnetic field.
