  Higgs boson production in association with a charm-quark jet proceeds through
two different mechanisms - one that involves the charm Yukawa coupling and the
other that involves direct Higgs coupling to gluons. The interference of the
two contributions requires a helicity flip and, therefore, cannot be computed
with massless charm quarks. In this paper, we consider QCD corrections to the
interference contribution starting from charm-gluon collisions with massive
charm quarks and taking the massless limit, $m_c \to 0$. The behavior of QCD
cross sections in that limit differs from expectations based on the canonical
QCD factorization. This implies that QCD corrections to the interference term
necessarily involve logarithms of the ratio $M_H/m_c$ whose resummation is
currently unknown. Although the explicit next-to-leading order QCD computation
does confirm the presence of up to two powers of $\ln(M_H/m_c)$ in the
interference contribution, their overall impact on the magnitude of QCD
corrections to the interference turns out to be moderate due to a cancellation
between double and single logarithmic terms.
