  Both reflected entropy and entanglement negativity provide valid measures of
entanglement between subsystems of a mixed state. For general 2D eternal black
holes coupled with CFT matters in large $c$ limit, we perform the replica-trick
computation and find that both effective Renyi reflected entropy and effective
entanglement negativity can be expressed in terms of the combination of
modified backreacting cosmic branes in $\mathrm{AdS}_3$ bulk. We then develop a
holographic scheme to calculate effective reflected entropy and entanglement
negativity for general 2D eternal black holes coupled with CFT matters in large
$c$ limit. Using the scheme, we check the consistency condition of the island
formulae for entanglement negativity and reflected entropy. We find that the
combinations of modified backreacting cosmic branes in $\mathrm{AdS}_3$ bulk
from the two island proposals of entanglement negativity exactly match with
each other. Finally, we study the saturation of the reflected entropy
inequality.
