A rigorous integral equation formulation in conjunction with Green's function theory is used to analyze the waveguiding and coupling phenomena in nonsymmetric (composed of dissimilar slabs) optical couplers with gratings etched on both slabs. The resulting integral equation is solved by applying an entire-domain Galerkin technique based on a Fourier series expansion of the unknown electric field on the grating regions. The proposed analysis actually constitutes a special type of the method of moments and provides high numerical stability and controllable accuracy. The singular points of the system's matrix accurately determine the complex propagation constants of the guided waves. The results obtained improve on those derived by coupled-mode methods in the cases of large grating perturbations and highly dissimilar slabs. Numerical results referring to the evolution of the propagation constants as a function of the grating's characteristics are presented. Optimal grating parameters with respect to minimum coupling length and maximum coupling efficiency are reported. The coupler's efficient operation as an optical bandpass filter is thoroughly investigated.