Routing in multi-hop wireless networks is a complex problem, especially in heterogeneous networks where multiple wireless communication technologies coexist. Reinforcement learning (RL) methods, such as Q-learning, have been introduced for decentralized routing by allowing nodes to make decisions based on local observations. However, Q-learning suffers from scalability issues and poor generalization due to the difficulty in managing the Q-table in large or dynamic network topologies, especially in heterogeneous networks (HetNets) with diverse channel characteristics. Thus, in this paper, we propose a novel deep Q-network (DQN)-based routing framework for heterogeneous multi-hop wireless networks to maximize the end-to-end rate of the route by improving scalability and adaptability, where each node uses a deep neural network (DNN) to estimate the Q-values and jointly select the next-hop relay and a communication technology for transmission. To achieve better performance with the DNN, selecting which nodes to exchange information is critical, as it not only defines the state and action spaces but also determines the input to the DNN. To this end, we propose neighbor node selection strategies based on channel gain and rate between nodes rather than a simple distance-based approach for an improved set of states and actions for DQN-based routing. During training, the model experiences diverse network topologies to ensure generalization and robustness, and simulation results show that the proposed neighbor node selection outperforms simple distance-based selection. Further, we observe that the DQN-based approach outperforms various benchmark schemes and performs comparably to the optimal approach.