Based on a proposed frame structure with an unequal sensing slot duration for each channel, and two sensing scenarios (with or without cooperation), a joint channel and sensing time assignment is suggested to maximize the uplink throughput of the centralized multi-band cognitive radio network with the consideration of the mutual interference among the secondary users (SUs). Firstly, the channel assignment is performed by using the proposed Delta Non-square Hungarian (DNH), which is a modified iterative Hungarian algorithm distinguished by throughput increment maximization and non-square weight matrix. Simulation results illustrate that DNH has significant advantages in enhancing the throughput and reducing the computational complexity. Moreover, a hybrid channel assignment, also performed by DNH, is improved based on the two sensing scenarios to maximize the throughput while efficiently limiting the interference power to primary users. Secondly, the convexity of the throughput functions within the range of sensing time is proved under the proposed frame structure, and then the maximum throughput is achieved through the steepest descent method-based sensing time assignment. Both of these results are corroborated by simulations.