When an observer's two eyes receive disparate stimulation, three possibilities may occur in the observer's visual consciousness: binocular rivalry, binocular transparency, and binocular composition. Here I demonstrate that the site of consciousness suppression in binocular rivalry must be monocular. I further suggest that binocular transparency is the maintenance in visual consciousness of two monocular images at different depth planes and that binocular fusion is a special case of binocular transparency where the two monocular images are maintained at the same depth plane. In this view, binocular rivalry, binocular transparency, and binocular composition constitutes a continuum of all possible percepts under dichoptic stimulation; in normal binocular viewing, for any depth plane either one monocular image or two monocular images (as in binocular composition) are represented in visual consciousness. Mapping onto the organization of human visual system, I suggest that the principal thalamic recipient layer 4C in primary visual cortex (V1) is the neural substrate for phenomenal visual consciousness and is a layered structured where visual surfaces are represented. Layer 4C has traditionally been viewed as the first stage of cortical visual processing, but I contend that this layer is the final stage of cortical computation for every episode of visual consciousness.