Due to the development of communication technology and the rise of user network demand, a reasonable resource allocation for wireless networks is the key to guaranteeing regular operation and improving system performance. Various frequency bands exist in the natural network environment, and heterogeneous cellular network (HCN) has become a hot topic for current research. Meanwhile, Reconfigurable Intelligent Surface (RIS) has become a key technology for developing next-generation wireless networks. By modifying the phase of the incident signal arriving at the RIS surface, RIS can improve the signal quality at the receiver and reduce co-channel interference. In this paper, we develop a RIS-assisted HCN model for a multi-base station (BS) multi-frequency network, which includes 4G, 5G, millimeter wave (mmwave), and terahertz networks, and considers the case of multiple network coverage users, which is more in line with the realistic network characteristics and the concept of 6G networks. We propose the optimization objective of maximizing the system sum rate, which is decomposed into two subproblems, i.e., the user resource allocation and the phase shift optimization problem of RIS components. Due to the NP-hard and coupling relationship, we use the block coordinate descent (BCD) method to alternately optimize the local solutions of the coalition game and the local discrete phase search algorithm to obtain the global solution. In contrast, most previous studies have used the coalition game algorithm to solve the resource allocation problem alone. Simulation results show that the algorithm performs better than the rest of the algorithms, effectively improves the system sum rate, and achieves performance close to the optimal solution of the traversal algorithm with low complexity.