The kinetics of material diffusion across an interface is analyzed wit
h special emphasis on the effect of the interface permeability on the
transport characteristics, such as the mean-square displacement and th
e residence probability in each of the two phases separated by the int
erface. Two practically important cases are considered, namely, one-di
mensional diffusion in a stepwise potential and three-dimensional diff
usion under a spherically symmetric square-well potential. The transpo
rt characteristics are shown to be independent of the permeability at
asymptotically long times, unless the interface is absolutely impermea
ble. However, the way the asymptotic behavior is approached can be con
trolled by the interface permeability. At low permeability values, the
kinetics exhibit a characteristic intermediate stage that can last fo
r such a long time that the true asymptotic behavior may not be observ
ed experimentally at all. Along with exact analytical solutions of the
diffusion problems at hand, useful approximate expressions are presen
ted for different stages of the kinetics.