  We study the effect of interlayer tunneling in the gauge theory describing a
quasi-two-dimensional paramagnetic metal close to a second-order or weakly
first-order antiferromagnetic phase boundary. In that theory, two species of
fermions have opposite (rather than equal) charges with respect to the gauge
field. We find that single-particle interlayer tunneling is suppressed at low
energies. The effect of pair tunneling is analyzed within the $(3-d)$
expansion. The resulting phase diagram has superconducting and non-Fermi-liquid
normal phases, and so is compatible with that of the copper-oxide
superconductors.
