Multihop packet routing is critical for unmanned aerial vehicle (UAV) networks to enable efficient communication between terminals in diverse environments. However, the complexity of routing design exacerbates due to interference from the environment and link instability caused by high-speed mobility. To address this challenge, we propose a harmonic function-based potential field to assess the impact of interference on UAV networks quantitatively. The proposed field maps the communication quality in terms of interference and mobility onto a virtual 3-D plane, providing a metric to establish routing paths. Based on this, two routing algorithms are designed to address two distinct routing requirements of UAV networks, timeliness and losslessness. Leveraging the natural adaptation to the potential field, the two proposed routing algorithms can effectively avoid interference while meeting different requirements. Simulation results demonstrate the effectiveness of the proposed potential field in representing the influences of interference and mobility. Additionally, the results validate the ability of the two routing algorithms to fulfill data communication requirements in terms of delay and accuracy while effectively mitigating interference.