This paper solves a plane strain problem for two bonded dissimilar planes containing two cracks parallel to the interface. The bimaterial system is loaded by tractions distributed along the crack surfaces. Based on the Fourier transform, the problem is reduced to a system of Cauchy-type singular integral equations that contain exact and explicit kernel functions. The solution of these equations are obtained easily by utilizing Gauss-Chebyshev formulae for various material combinations and geometrical parameters. Several numerical examples of stress intensity factors, energy release rates, and crack opening displacement are presented to exhibit the interactions among the interface and cracks.