  Interfacial spin-flip scattering plays an important role in magnetoelectronic
devices. Spin loss at metallic interfaces is usually quantified by matching the
magnetoresistance data for multilayers to the Valet-Fert model, while treating
each interface as a fictitious bulk layer whose thickness is $\delta$ times the
spin-diffusion length. By employing the properly generalized circuit theory and
the scattering matrix approaches, we derive the relation of the parameter
$\delta$ to the spin-flip transmission and reflection probabilities at an
individual interface. It is found that $\delta$ is proportional to the square
root of the probability of spin-flip scattering. We calculate the spin-flip
transmission probability for flat and rough Cu/Pd interfaces using the
Landauer-B\"uttiker method based on the first-principles electronic structure
and find $\delta$ in reasonable agreement with experiment.
