  We use quantum Monte Carlo to determine the magnetic and transport properties
of coupled square lattice spin and fermionic planes as a model for a
metal-insulator interface. Specifically, layers of Ising spins with an
intra-layer exchange constant $J$ interact with the electronic spins of several
adjoining metallic sheets via a coupling $J_H$. When the chemical potential
cuts across the band center, that is, at half-filling, the N\'eel temperature
of antiferromagnetic ($J>0$) Ising spins is enhanced by the coupling to the
metal, while in the ferromagnetic case ($J<0$) the metallic degrees of freedom
reduce the ordering temperature. In the former case, a gap opens in the
fermionic spectrum, driving insulating behavior, and the electron spins also
order. This induced antiferromagnetism penetrates more weakly as the distance
from the interface increases, and also exhibits a non-monotonic dependence on
$J_H$. For doped lattices an interesting charge disproportionation occurs where
electrons move to the interface layer to maintain half-filling there.
