Satellite-terrestrial integrated networks (STINs) are considered to be a new paradigm for the next generation of global communication because of its distinctive merits, such as wide coverage, high reliability, and flexibility. When the satellite associates with different base stations (BSs) and adopts different channels for communication, the utility of offloading data to BSs is different. In our work, we study how to jointly associate satellites with appropriate BSs and allocate channels to satellites. Our purpose is to maximize the utility of the data offloaded from satellites to BSs while considering the load balance of BSs. However, some satellites are often unable to connect to BSs because of their periodic flight characteristic, which makes the joint satellite-BS association and channel allocation more challenging. To solve the problem that satellites sometimes cannot connect to BSs, we abstract the communication model between satellites and BSs into a bipartite graph and add a virtual BS to ensure that all satellites can connect to at least one BS. Then, in the constructed joint optimization problem, we solve the assignment of satellites and channels simultaneously. Considering that the joint optimization problem is nonconvex, we use double deep Q-Network (DDQN) for achieving the optimal strategy of satellite association and channel allocation. Furthermore, the reward value in most state transition information generated by satellites is 0, which leads to the low learning efficiency of DDQN. Aiming at enhancing the learning efficiency of DDQN, the priority sampling-based DDQN (PSDDQN) algorithm is proposed. Experimental results demonstrate that PSDDQN gets better utility and achieves the load balance of BSs compared with other algorithms.