  Transport in superconducting heterostructures is very successfully described
with quasiclassical Green's functions augmented by microscopically derived
boundary conditions. However, so far the spin-dependence is in the diffusive
approach included only for limiting cases. Here, we derive the fully
spin-dependent boundary condition completing the Usadel equation and the
circuit theory. Both, material specific spin-degrees of freedom and
spin-dependent interface effects, i.e. spin-mixing and polarization of the
transmission coefficients are treated exactly. This opens the road to
accurately describe a completely new class of mesoscopic circuits including
materials with strong intrinsic magnetic structure. We also discuss several
experimentally relevant cases like the tunnel limit, a ferromagnetic insulator
with arbitrarily strong magnetization and the limit of small spin-mixing.
