  The QCD$\times$QED factorization is studied for two-body non-leptonic and
semi-leptonic $B$ decays with heavy-light final states. These non-leptonic
decays, like $\bar{B}^0_{(s)}\to D^+_{(s)} \pi^-$ and $\bar{B}_d^0 \to D^+
K^-$, are among the theoretically cleanest non-leptonic decays as penguin loops
do not contribute and colour-suppressed tree amplitudes are suppressed in the
heavy-quark limit or even completely absent. Advancing the theoretical
calculations of such decays requires therefore also a careful analysis of QED
effects. Including QED effects does not alter the general structure of
factorization which is analogous for both semi-leptonic and non-leptonic
decays. For the latter, we express our result as a correction of the tree
amplitude coefficient $a_1$. At the amplitude level, we find QED effects at the
sub-percent level, which is of the same order as the QCD uncertainty. We
discuss the phenomenological implications of adding QED effects in light of
discrepancies observed between theory and experimental data, for ratios of
non-leptonic over semi-leptonic decay rates. At the level of the rate,
ultrasoft photon effects can produce a correction up to a few percent,
requiring a careful treatment of such effects in the experimental analyses.
