We provide a derivation of bidirectional coupled-mode equations from Maxwell's equations. The theoretical description of the collinear magneto-optical interaction of magnetostatic forward volume waves with guided optical modes is generalized. Its behavior is expressed using solutions to the coupled-mode equations. In some cases, applying the conservation of energy yields exact solutions that can be formed in terms of elementary transcendental functions. The auxiliary function method is used to find a series solution based on the solution of the homogeneous boundary value problem. Using the derived solutions, simulations show that the parallel antiparallel magneto-optical interaction bandwidth and structure can be tuned through selection of power applied to two transducers. They also show that equivalent mode power conversion can take place in half the propagation distance for parallel anitparallel magneto-optical interaction compared to pure traveling wave magneto-optical interaction.