We look at the possibility of spatially indirect exciton condensation 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
conveniently 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