Unmanned aerial vehicle (UAV) relay networks are convinced to be a significant complement to terrestrial infrastructures to provide robust network capacity. However, most of the existing works either considered enhanced mobile broadband (eMBB) payload communication or ultra-reliable and low latency communications (URLLC) control information communication. In this paper, we investigate resource allocation for the eMBB payload and URLLC control information communication multiplexing in a multi-UAV relay network. We firstly propose a multi-UAV relay model comprehensively considering path loss, small-scale channel fading and different quality of service requirements of eMBB and URLLC communications. Then we formulate the multiplexing problem as a joint user association, bandwidth and transmit power optimization problem to improve total transmission data rate and reduce power consumption. The solution of this problem is challenging due to different capacity characteristics of eMBB and URLLC communications, the coupling of continuous variables and integer variables, and the non-convexity. To mitigate these challenges, we equivalently decompose the original optimization problem into a URLLC problem and an eMBB problem. For the URLLC problem, we derive closed-form expressions of the optimal bandwidth and transmit power. For the eMBB problem, we develop an iterative solution framework of alternatively optimizing user association, bandwidth and transmit power.