Mixed-mode fractures of arbitrary orientation with respect to a planar bimaterial interface have been effectively modelled using a surface integral approach. By requiring only that the surface of the fracture be discretized, the surface integral method circumvents the practical difficulties associated with having to mesh the interacting dual singularities in stress along the three-dimensional (3-D) crack front and at the interface. The key elements of this numerical capability are discussed in detail. These include: the derivation of the fundamental solutions for a generalized fracture event near a planar bimaterial interface, formulation of the governing integral equation including its decomposition into singular and non-singular terms, development of analytical and numerical techniques for performing the singular integrations, and efficient numerical integration of the non-singular terms using non-dimensionalized surface approximations of the dipole solutions. The problem of a pressurized planar crack near a bimaterial interface was used to assess convergence. The effect of material contrast and crack shape on tendencies for crack growth were also examined.