Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.