In this paper, we address the problem of scheduling and routing design in a multi-hop heterogeneous radio network. The scenario consists of two types of nodes: scheduled nodes, which depend upon a centralised resource scheduling scheme, and uncoordinated nodes, which employ an asynchronous Carrier Sense Multiple Access (CSMA) based medium access control protocol. Both types of nodes co-exist on the same spectrum and may interfere each other. In fact, scheduled nodes are synchronized to the Base Station (BS) and communicate to it in a multi-hop fashion, while uncoordinated users are asynchronous with respect to the BS and the other nodes. Our work focuses on the problem of routing and scheduling for the scheduled set of nodes, with the aim of avoiding interference caused by CSMA nodes. In particular, we propose a Coexistence-Aware (CA) routing scheme, based on the definition of a novel link cost metric accounting for the number of potential uncoordinated nodes interfering. The output of the CA routing scheme serves an input to a Multi-Link Proportional Fair (MLPF) scheme, where a new scheduling metric, accounting for the number of hops needed to reach the BS, is designed. The proposed algorithm is compared with a benchmark solution, where routing is based on the level of received power over the links and where the MLPF algorithm presented in the literature is applied. Results show the improvement achieved with the proposed solution.