The multiband method has been extended to treat the resonance interference effect between two nuclides based on the intermediate resonance approximation. The integral equation of the flux belonging to different bands of the two nuclides is derived for a heterogeneous cell system. In the equation, a new band parameter is introduced. The new parameter denotes the conditional probability that a nuclide takes a certain band under the condition that the other nuclide takes another band. The calculational procedure of band parameters is described in a homogeneous medium. This method has been applied to a homogeneous medium and a thermal reactor cell containing 235U and 238U. The effective cross sections calculated by this method and the conventional multiband method without considering the interference effect are compared with the results by a reference continuous-energy Monte Carlo method. It is seen that the conventional multiband method greatly overestimates the fission and capture cross sections of 235U for energy groups where there are both resonances of 235U and 238U, and the present method remarkably improves the overestimation.