Much progress has been made in understanding how the brain combines signals from the two eyes. However, most of this work has involved achromatic (black and white) stimuli, and it is not clear if the same processes apply in color-sensitive pathways. In our first experiment, we measured contrast discrimination ("dipper") functions for four key ocular configurations (monocular, binocular, half-binocular, and dichoptic), for achromatic, isoluminant L-M and isoluminant S-(L+M) sine-wave grating stimuli (L: long-, M: medium-, S: short-wavelength). We find a similar pattern of results across stimuli, implying equivalently strong interocular suppression within each pathway. Our second experiment measured dichoptic masking within and between pathways using the method of constant stimuli. Masking was strongest within-pathway and weakest between S-(L+M) and achromatic mechanisms. Finally, we repeated the dipper experiment using temporal luminance modulations, which produced slightly weaker interocular suppression than for spatially modulated stimuli. We interpret our results in the context of a contemporary two-stage model of binocular contrast gain control, implemented here using a hierarchical Bayesian framework. Posterior distributions of the weight of interocular suppression overlapped with a value of 1 for all dipper data sets, and the model captured well the pattern of thresholds from all three experiments.