A microscopic model of the proximity effect in superconductor-insulator-superconductor (SS’IS’’S) Josephson tunnel junctions has been developed for the general case of the finite critical temperature of the S’(S’’) metal, arbitrary SS’(SS’’) boundary transparency and the strength of the proximity effect between S and S’(respectively S and S’’). The metals are assumed to be in the dirty limit and the thickness of the proximity layer is assumed to be small compared to its coherence length. The electrical properties of the SS’IS’’S junction are calculated as a function of the strength of the proximity effect, boundary transparency, critical temperature ratio, and temperature. The experimentally determined electrical characteristics of a series of Nb/Al 1, Al oxide, Al 2/Nb junctions with varying thickness d 1 of the Al 1 layer were interpreted with this model. The current-voltage characteristics and the temperature dependence of the critical current and sum-gap voltage could be described quantitatively well without any other correction than the non-BCS ratio Δ 0/k B T c≊ 1.93 of Nb. Deviations from the model for the junctions with the largest d 1 are attributed to the fact that the Nb and Al are not fully in the dirty limit and d 1 is not small compared to the coherence length.