  We investigate the transport properties of a junction consisting of an
electron-hole bilayer in contact with normal and superconducting leads. The
electron-hole bilayer is considered as a semi-metal with two electronic bands.
We assume that in the region between the contacts the system hosts an exciton
condensate described by a BCS-like model with a gap $\Gamma$ in the
quasiparticle density of states. We first discuss how the subgap electronic
transport through the junction is mainly governed by the interplay between two
kinds of reflection processes at the interfaces: The standard Andreev
reflection at the interface between the superconductor and the exciton
condensate, and a coherent crossed reflection at the
semi-metal/exciton-condensate interface that converts electrons from one layer
into the other. We show that the differential conductance of the junction shows
a minimum at voltages of the order of $\Gamma/e$. Such a minimum can be seen as
a direct hallmark of the existence of the gapped excitonic state.
