Through conversation, humans relay complex information through the alternation of speech production and comprehension. The neural mechanisms that underlie these complementary processes or through which information is precisely conveyed by language, however, remain poorly understood. Here, we used pretrained deep learning natural language processing models in combination with intracranial neuronal recordings to discover neural signals that reliably reflect speech production, comprehension, and their transitions during natural conversation between individuals. Our findings indicate that neural activities that encoded linguistic information were broadly distributed throughout frontotemporal areas across multiple frequency bands. We also find that these activities were specific to the words and sentences being conveyed and that they were dependent on the word's specific context and order. Finally, we demonstrate that these neural patterns partially overlapped during language production and comprehension and that listener-speaker transitions were associated with specific, time-aligned changes in neural activity. Collectively, our findings reveal a dynamical organization of neural activities that subserve language production and comprehension during natural conversation and harness the use of deep learning models in understanding the neural mechanisms underlying human language.