This letter investigates covert routing communications in a heterogeneous network where a source transmits confidential data to a destination with the aid of relaying nodes where each transmitter judiciously chooses one modality among multiple communication modalities. We develop a novel reinforcement learning-based covert routing algorithm that finds a route from the source to the destination where each node identifies its next hop and modality only based on the local feedback information received from its neighboring nodes. We show based on numerical simulations that the proposed covert routing strategy has only negligible performance loss compared to the optimal centralized routing scheme.