The three-dimensional M-integral is presented for calculating stress intensity factors for an interface crack between two fiber reinforced materials which are treated effectively as transversely isotropic materials. The material in the upper half-space is in the +45°-direction, whereas the material in the lower half-space is in the -45°-direction. An interface crack in this material possesses oscillatory and square-root singularities. A test case of a three-dimensional bimaterial slab containing an edge interface crack is described. The first term of the asymptotic displacement field is applied with the complex stress intensity factor K = 0 and mode II stress intensity factor KII = 1 on the outer boundaries of the body. The crack faces are traction free. Solution to this problem, should be precisely the imposed stress intensity factor. Excellent results are obtained. Other test problems, not presented here, also produce excellent results.