In this work, we investigate the routing and channel assignment problem in Self-Interference Suppression (SIS)-enabled CRNs, where FD communication is possible. Specifically, we propose a novel metric called “Path Capacity” that reflects the number of links that can be simultaneously activated across a given path while using the minimum possible spectrum resources. Accordingly, we develop a novel routing scheme that selects the best path along with the channel assignment such that the highest capacity is achieved. We analytically formulate the routing problem as a route selection and channel assignment optimization, with the objective of minimizing the required number of distinct channels for each CR source-destination pair. We show that the optimization problem is a Binary Quadratic Programming (BQP) problem, which is, in general, NP-hard. Accordingly, we present a sequential fixing procedure that provides a near-optimal solution. Simulation results are provided, which show that a careful routing and channel assignment in SIS-enabled CRNs can significantly improve network performance.