  We obtain the reflected entropy for bipartite mixed state configurations
involving two disjoint and adjacent subsystems in two dimensional boundary
conformal field theories (BCFT$_2$s) in a black hole background. The bulk dual
is described by an AdS$_3$ black string geometry truncated by a Karch-Randall
brane. The entanglement wedge cross section computed for this geometry matches
with the reflected entropy obtained for the BCFT$_2$ verifying the holographic
duality. In this context, we also obtain the analogues of the Page curves for
the reflected entropy and investigate the behaviour of the Markov gap.
