  It is usually believed that the spin-fluctuation mechanism for
high-temperature superconductivity results in d-wave pairing, and that it is
destructive for the conventional phonon-mediated pairing. We show that in
bilayer materials, due to nearly perfect antiferromagnetic spin correlations
between the planes, the stronger instability is with respect to a
superconducting state whose order parameters in the even and odd plane-bands
have opposite signs, while having both two-dimensional $s$-symmetry. The
interaction of electrons with Raman- (infrared-) active phonons enhances
(suppresses) the instability.
