This paper develops a communication-efficient distributed mapping approach for rapid exploration of a cave by a multi-robot team. Subsurface planetary exploration is an unsolved problem challenged by communication, power, and compute constraints. Prior works have addressed the problems of rapid exploration and leveraging multiple systems to increase exploration rate; however, communication considerations have been left largely unaddressed. This paper bridges this gap in the state of the art by developing distributed perceptual modeling that enables high-fidelity mapping while remaining amenable to low-bandwidth communication channels. The approach yields significant gains in exploration rate for multi-robot teams as compared to state-of-the-art approaches. The work is evaluated through simulation studies and hardware experiments in a wild cave in West Virginia.