We calculate the two-pion correlation function for an expanding hadron source with a finite baryon density. The space-time evolution of the source is described by relativistic hydrodynamics and the Hanbury-Brown-Twiss (HBT) radius is extracted after effects of collective expansion and multiple scattering on the HBT interferometry have been taken into account, using quantum probability amplitudes in a path-integral formalism. We find that this radius is substantially smaller than the HBT radius extracted from the freeze-out configuration.