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This paper focuses on the development of a new mathematical model and its analytical solution for the analysis of the mechanical behavior of geometrically and materially linear three-dimensional two-layer bimetallic beams with interface compliance. Consequently, the analytical solution of bending of elastic three-dimensional two-layer composite beams with interface compliance is derived for the first time. In the illustrative example, a three-dimensional two-layer cantilever composite beam made of 6061-T6 aluminum and C83400 red brass is analyzed. It is shown that interface compliance could have a significant influence on the mechanical behavior of such a structure. Finally, the results for different mechanical quantities are tabulated and as such the analytical solution presented can be used as a benchmark solution of three-dimensional bimetallic composite beams.