  We study the effect of the interfacial transparency on the Josephson current
in a diffusive ferromagnetic contact between two superconductors. In contrast
to the cases of the fully transparent and the low-transparency interfaces, the
current-phase relation is shown to be nonsinusoidal for a finite transparency.
It is demonstrated that even for the nearly fully transparent interfaces the
small corrections due to weak interfacial disorders contribute a small
second-harmonic component in the current-phase relation. For a certain
thicknesses of the ferromagnetic contact and the exchange field this can lead
to a tiny minimum supercurrent at the crossover between 0 and $\pi$ states of
the junction. Our theory has a satisfactory agreement with the recent
experiments in which a finite supercurrent was observed at the transition
temperature. We further explain the possibility for observation of a large
residual supercurrent if the interfaces have an intermediate transparency.
