  The single band, two dimensional Hubbard Hamiltonian has been extensively
studied as a model for high temperature superconductivity. While Quantum Monte
Carlo simulations within the dynamic cluster approximation are now providing
considerable evidence for a d-wave superconducting state at low temperature,
such a transition remains well out of reach of finite lattice simulations
because of the "sign problem". We show here that a bilayer Hubbard model, in
which one layer is electron doped and one layer is hole doped, can be studied
to lower temperatures and exhibits an interesting signal of d-wave pairing. The
results of our simulations bear resemblance to a recent report on the magnetic
and superconducting properties of Ba$_2$Ca$_3$Cu$_4$O$_8$F$_2$ which contains
both electron and hole doped CuO$_2$ planes. We also explore the phase diagram
of bilayer models in which each sheet is at half-filling.
