Spectrum-efficient routing has been subject to interest in the recent literature. The underlying scheduling scheme, however, assumes interference is harmful and concurrent neighboring transmissions are forbidden, and thus the Spectral Efficiency (SE) performance is restricted to some extent. In this paper, we propose a novel joint routing and scheduling scheme with Successive Interference Cancellation (SIC) to exploit interference in multihop wireless networks, such that the SE can be greatly improved. Specifically, we first devise an interesting transmission strategy that applies SIC to explore concurrent neighboring transmission opportunities on an arbitrary path. To maximize the SE benefit brought by concurrent neighboring transmissions, two low-complexity routing algorithms are then presented. Furthermore, based on theoretical analysis, closed-form expressions of approximate SE bound are derived and shown to be very accurate in terms of key network parameters. Numerous simulation results verify that significant SE gains can be obtained through SIC.