How does the human brain combine information across the eyes? It has been known for many years that cortical normalization mechanisms implement ‘ocularity invariance’: equalizing neural responses to spatial patterns presented either monocularly or binocularly. Here, we used a novel combination of electrophysiology, psychophysics, pupillometry, and computational modeling to ask whether this invariance also holds for flickering luminance stimuli with no spatial contrast. We find dramatic violations of ocularity invariance for these stimuli, both in the cortex and also in the subcortical pathways that govern pupil diameter. Specifically, we find substantial binocular facilitation in both pathways with the effect being strongest in the cortex. Near-linear binocular additivity (instead of ocularity invariance) was also found using a perceptual luminance matching task. Ocularity invariance is, therefore, not a ubiquitous feature of visual processing, and the brain appears to repurpose a generic normalization algorithm for different visual functions by adjusting the amount of interocular suppression.