  We demonstrate that perfect conversion between charged supercurrents in
superconductors and neutral supercurrents in electron-hole pair condensates is
possible via a new Andreev-like scattering mechanism. As a result, when two
superconducting circuits are coupled through a bilayer exciton condensate, the
superflow in both layers is drastically modified. Depending on the phase biases
the supercurrents can be completely blocked or exhibit perfect drag.
