The authors examine both codirectional and contradirectional nonlinear couplers operating by second harmonic generation with particular attention to the effect of linear and nonlinear phase mismatches under the assumption that the second harmonic mode is stimulated by a strong coherent field. Quantum statistical properties are described by a photocount distribution, its factorial moments, quadrature and integrated intensity variances and the uncertainty product, with particular attention to generation and transmission of nonclassical light. Incident beams can be coherent or squeezed with mixed external noise. It is shown that, in general, the nonlinear phase mismatch, which effectively makes the interaction weaker, may reduce nonclassical effects and their transmission to signal linear waveguide. However, as a consequence of the phase mismatches some initial regimes of the interaction can be repeated, which leads to new interesting nonclassical effects.