We produce transmission and reflection spectra of the anti-directional coupler (ADC) composed of linearly coupled positive- and negative-refractive-index arms, with intrinsic Kerr nonlinearity. Both reflection and transmission feature two highly amplified peaks at two distinct wavelengths in a certain range of values of the gain, making it possible to design a wavelength-selective mode-amplification system. We also predict that a blend of gain and loss in suitable proportions can robustly enhance reflection spectra that are detrimentally affected by the attenuation, in addition to causing red and blue shifts owing to the Kerr effect. In particular, ADC with equal gain and loss coefficients is considered in necessary detail.