  We investigate the production of Higgs bosons in neutral- and charged-current
interactions at a future Muon-Ion Collider (MuIC) with emphasis on $H^0 \to
c\overline{c}$ decay. In particular, we focus on the leading production
mechanisms and explore the impact of a range of Parton Distribution Function
(PDF) scenarios, with emphasis on the role of heavy intrinsic quark flavor. We
emphasize estimates of non-resonant di-charm background production and explore
the impact of this background on a possible future measurement of $H^0 \to
c\overline{c}$ at a future Muon-Ion Collider facility.
