Fixed-point models have already been successfully used to analytically study networks consisting of persistent TCP flows only, or mixed TCP/UDP flows with a single queue per link and differentiated buffer management for these two types of flows. In the current study, we propose a nested fixed-point analytical method to obtain the throughput of persistent TCP and UDP flows in a network of routers supporting class-based weighted fair queuing allowing the use of separate queues for each class. In particular, we study the case of two classes where one of the classes uses drop-tail queue management and is intended for only UDP traffic. The other class targeting TCP, but also allowing UDP traffic for the purpose of generality, is assumed to employ active queue management. The effectiveness of the proposed analytical method is validated in terms of accuracy using ns-3 simulations and the required computational effort.