Interference limits the throughput of modern wireless communication networks, and thus the successful mitigation of interference can have a significant impact on network performance. Successive interference cancellation (SIC) has emerged as a promising physical layer method, where multiple packets received simultaneously need not be treated as a ``collision'' requiring retransmission; rather, under certain conditions, all of the packets can be decoded. Obviously, using SIC can thus serve as an important design element that can provide higher performance for the network. However, it also requires a rethinking of the way that traditional routing and scheduling algorithms, which are designed for a traditional physical layer, are developed. In order to consider routing and scheduling over a physical layer employing SIC, some tools such as the oft-employed conflict graph need to be modified. In particular, a notion of links interfering with other links ``indirectly'' is required, and this issue has been ignored in many past works. Therefore, considering the dependencies and interferences between links, a joint routing and scheduling algorithm that employs an understanding of the SIC that will be employed at the physical layer is presented and shown to surpass previous algorithms. We know that the maximum throughput scheduling problem is NP-hard. On the other hand, even if we can reach maximum throughput scheduling, while being throughput efficient, it can result in highly unfair rates among the users. Hence, proportional fairness is developed in the proposed algorithm.