  We investigate the possibility and implications of interlayer coherence in
electrically isolated superconducting bilayers. We find that in a mean-field
approximation bilayers can have superconducting and excitonic order
simultaneously if repulsive interactions between layers are sufficiently
strong. The excitonic order implies interlayer phase coherence, and can be
studied in a representation of symmetric and antisymmetric bilayer states. When
both orders are present we find several solutions of the mean-field equations
with different values of the the symmetric and antisymmetric state pair
amplitudes. The mixed state necessarily has non-zero pair amplitudes for
electrons in different layers in spite of the repulsive interlayer
interactions, and these are responsible for spatially indirect Andreev
reflection processes in which an incoming electron in one layer can be
reflected as a hole in the opposite layer. We evaluate layer diagonal and
off-diagonal current-voltage relationships that can be used to identify this
state experimentally.
