  We present a theoretical study of the quasiparticle and subgap conductance of
generic $X/I_{sf}/S_{M}$ junction with a spin-filter barrier $I_{sf}$, where
$X$ is either a normal $N$ or a ferromagnetic metal $F$ and $S_{M}$ is a
superconductor with a built-in exchange field. Our study is based on the
tunneling Hamiltonian and the Green's function technique. First, we focus on
the quasiparticle transport, both above and below the superconducting critical
temperature. We obtain a general expression for the tunneling conductance which
are valid for arbitrary values of the exchange field and arbitrary
magnetization directions in the electrodes and in the spin-filter barrier. In
the second part we consider the subgap conductance of a normal
metal-superconductor junction with a spin-filter barrier. We provide a
heuristic derivation of new boundary conditions for the quasiclassical Green's
functions which take into account the spin-filter effect at the interface. With
the help of these boundary conditions, we show how the proximity effect and the
subgap conductance is suppressed by spin-filtering in a $N/I_{sf}/S$ junction,
where $N$ is a normal metal. Our work provides useful tools for the study of
spin-polarized transport in hybrid structures both in the normal and the
superconducting state.
