Investigations into the neural basis of conscious perception span multiple scales and levels of analysis. There is, however, a theoretical and methodological gap between advances made at the microscopic scale in animals and those made at the macroscopic scale in cognitive neuroscience. This divide constrains the neurobiological understanding of conscious perception to the scale of each specific measurement modality. Here, we use computational modelling to bridge this divide. Specifically, we show that the same (microscopic) mechanism that underlies conscious perception in a mouse model of threshold perception – namely, apical dendrite mediated burst firing in thick-tufted layer V pyramidal neurons – determines perceptual dominance in a thalamocortical spiking neural network model of visual rivalry – a staple paradigm in the (macroscopic) cognitive neuroscience of consciousness. The model conforms to the constraints imposed by decades of previous research into visual rivalry in human and non-human primates and explains the slowing of perceptual reversals caused by genetic perturbations to E/I balance in a mouse model of visual rivalry. In addition, the model’s layer-specific structure and thalamocortical connectivity allowed us to simulate both cellular level (optogenetic and pharmacological) interventions and the downstream neuronal effects of psychological manipulations of attention and expectation. Our model, therefore, provides an empirically-tractable bridge between cellular-level mechanisms and conscious perception.