Networks need to accommodate diverse applications with different Quality-of-Service (QoS) requirements. New ideas at the physical layer are being developed for this purpose, such as diversity embedded coding, which is a technique that combines high rates with high reliability. We address the problem of how to fully utilize different rate-reliability characteristics at the physical layer to support different types of traffic over a network and to jointly maximize their utilities. We set up a new framework based on utility maximization for networks with composite links, meaning that each link consists of sub-links that can attain different rate-reliability characteristics simultaneously. We incorporate delay, in addition to rate and reliability, into the utility functions. To accommodate different types of traffic, we propose distributed algorithms for the optimal rate-reliability-delay tradeoff based on capacity division and priority queueing. Numerical results show that compared with traditional codes, the new codes can provide higher network utilities for all traffic types simultaneously. The results also show that priority queueing achieves higher network utility than capacity division.