Boundary conformal field theory (BCFT) and interface conformal field theory (ICFT) attract attention in the context of the information paradox problem. On this background, we develop the idea of the reflected entropy in BCFT/ICFT. We first introduce the left-right reflected entropy (LRRE) in BCFT and show that its holographic dual is given by the area of the entanglement wedge cross section (EWCS) through AdS/BCFT. We also present how to evaluate the reflected entropy in ICFT. By using this technique, we can show the universal behavior of the Markov gap in some special cases. Furthermore, we clarify what is the holographic dual of boundary primary correlation functions by using this LRRE/EWCS duality.