  We explain the strong interlayer drag resistance observed at low temperatures
in bilayer electron-hole systems in terms of an interplay between local
electron-hole-pair condensation and disorder-induced carrier density
variations. Smooth disorder drives the condensate into a granulated phase where
interlayer coherence is formed only in well separated and disconnected regions,
or grains, and the densities of electrons and holes accidentally match. The
drag resistance is then dominated by Andreev scattering of charge carries
between layers at the grains that transfers momentum between layers. We show
that this scenario can account for the observed dependence of the drag
resistivity on temperature, and on the average charge imbalance between layers.
