  We extend the Mellin representation of conformal field theory (CFT) to allow
for conformal boundaries and interfaces. We consider the simplest holographic
setup dual to an interface CFT - a brane filling an $AdS_{d}$ subspace of
$AdS_{d+1}$ - and perform a systematic study of Witten diagrams in this setup.
As a byproduct of our analysis, we show that geodesic Witten diagrams in this
geometry reproduce interface CFT$_d$ conformal blocks, generalizing the
analogous statement for CFTs with no defects.
