  We present a first-principles investigation of the electronic and optical
properties of hybrid organic-inorganic interfaces consisting of MoS$_2$
monolayer and the $\pi$-conjugate molecules pyrene and pyridine. For both
hybrid systems, the quasi-particle band structure obtained from the $G_0W_0$
approximation shows -- in contrast to density-functional theory -- level
alignment of type II, owing to the mutual dynamical screening of the interface
constituents. $\textit{Ab initio}$ calculations of the absorption spectrum
based on the Bethe-Salpeter equation reveal besides intra-layer excitons on the
MoS$_2$ side, hybrid as well as charge-transfer excitons at the interface.
These findings indicate that hybrid systems consisting of semiconducting
transition-metal dichalcogenides and organic $\pi$-conjugate molecules can host
a rich variety of optical excitations and thus provide a promising venue to
explore many-body interactions and exciton physics in low dimensionality.
