  We study the physical properties of a half-metallic
ferromagnet$\mid$superconductor (HM$\mid$S) bilayer, allowing for an arbitrary
bulk pairing symmetry of the superconductor and spin-dependent processes at the
interface. In particular, we study how the possibility of unconventional
pairing such as $p$- and d-wave and a spin-active interface influence the
\textit{(i)} conductance spectra, \textit{(ii)} proximity effect, and
\textit{(iii)} local density of states of such a bilayer. Our calculation is
done both analytically and numerically in the ballistic limit, using both a
continuum- and lattice-model. It is found that the spin-dependent phase-shifts
occuring at the HM$\mid$S interface seriously influence all of the
aforementioned phenomena. We explain our results in terms of Andreev reflection
in the presence of a spin-active interface, allowing for both spin-filtering
and spin-mixing processes. We demonstrate how the surface-bound states induced
by the anisotropy of the superconducting order parameter at the HM$\mid$S
interface are highly sensitive to these spin-dependent processes. Our results
can be directly tested experimentally using STM-measurements and/or
point-contact spectroscopy.
