Currently, wireless body area networks (WBANs) are effectively used for health monitoring services. However, in cases where WBANs are densely deployed, interference among WBANs can cause serious degradation of network performance and reliability. Inter-WBAN interference can be reduced by scheduling the communication links of interfering WBANs. In this paper, we propose an interference-aware traffic-priority-based link scheduling (ITLS) algorithm to overcome inter-WBAN interference in densely deployed WBANs. First, we model a network with multiple WBANs as an interference graph where node-level interference and traffic priority are taken into account. Second, we formulate link scheduling for multiple WBANs as an optimization model where the objective is to maximize the throughput of the entire network while ensuring the traffic priority of sensor nodes. Finally, we propose the ITLS algorithm for multiple WBANs on the basis of the optimization model. High spatial reuse is also achieved in the proposed ITLS algorithm. The proposed ITLS achieves high spatial reuse while considering traffic priority, packet length, and the number of interfered sensor nodes. Our simulation results show that the proposed ITLS significantly increases spatial reuse and network throughput with lower delay by mitigating inter-WBAN interference.