Cracking the neural code is to attribute proper meaning to temporal sequences of action potentials. While the neural code is typically understood as a set of rules to translate features of the external world into trains of action potentials, anatomical connections show that external input is often combined with internal signals from higher order areas. A popular view poses that this top-down input merely modulates the encoding of bottom-up information, a signal fusion that leads to an information loss with respect to the two individual signals. Based on the known properties of cortical neurons and circuits, we suggest that, instead, both signals are represented simultaneously, in the form of a multiplexed population code consisting of spikes and bursts. We use a computational model of thick-tufted pyramidal neurons that is constrained by data to understand how bottom-up and top-down signals are represented in the spiking activity of a population. We show that top-down signals arriving in distal dendrites are represented by the relative prevalence of bursts, while bottom-up information arriving perisomatically is encoded in the sum of single spikes and bursts. Using a coherence-based information-theoretical analysis, we show that the code can more than double the rate of information transfer, even for rapidly changing signals. We then show that both bottom-up and top-down signals can also be decoded by biologically plausible mechanisms, namely by combining inhibitory microcircuits with short-term plasticity. These results suggest a novel functional role of both active dendrites and the stereotypical patterns with which inhibitory cell types interconnect in the neocortex. Burst ensemble multiplexing, we suggest, is a general code used by the nervous system to flexibly combine two distinct streams of information.