  We study the k-dependence of the gap function of a bilayer superconductor,
using standard mean-field techniques applied to a 2D extended Hubbard model, in
the presence of coherent interlayer pair-tunneling and quenched coherent
single-particle tunneling. The intralayer pairing potential thus defined is
expandable in a finite number of basis functions for the irreducible
representations of the point-group of the perfectly square lattice, C_{4v}.
  This gives rise to a competition between s- and d-wave symmetry, as the
chemical potential is increased from the bottom to the top of a realistic band
for most cuprates. It allows for mixed-symmetry paired state at temperatures
below T_c, but never at T_c on a square lattice. Inclusion of the interlayer
pair-tunneling into the effective pairing potential leads to highly non-trivial
k-space structures, such as pronounced maxima along the Fermi line not seen in
the absence of interlayer pair-tunneling.
  We show how such a gap structure evolves with temperature and with band
filling, and how it affects various observables. In particular, a nonuniversal
value of the normalized jump in the specific heat at T_c will be evidenced, at
variance with the conventional universal BCS result.
