  We investigate the reflected entropy for various mixed state configurations
in the two dimensional holographic conformal field theories sharing a common
interface (ICFTs). In the AdS$_3$/ICFT$_2$ framework, we compute the
holographic reflected entropy for the required configurations in the vacuum
state of the ICFT$_{\text{2}}$ which is given by twice the entanglement wedge
cross section (EWCS) in a spacetime involving two AdS$_3$ geometries glued
along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk
geometry involving eternal BTZ black strings with an AdS$_2$ interface brane,
which is dual to an ICFT$_2$ in the thermofield double (TFD) state. We explore
the system from a doubly holographic perspective and determine the island
contributions to the reflected entropy in the two dimensional semi-classical
description involving two CFT$_{\text{2}}$s coupled to an AdS$_2$ brane. We
demonstrate that the results from the island formula match precisely with the
bulk AdS$_3$ results in the large tension limit of the interface brane. We
illustrate that the phase structure of the reflected entropy is quite rich
involving many novel induced island phases and demonstrate that it obeys the
expected Page curve for the reflected entropy in a radiation bath coupled to
the AdS$_2$ black hole.
