The sixth-generation (6G) communication technology is expected to provide the seamless and ubiquitous wireless access for future cellular networks. Due to the rise of network demands and the limited communication resource, the multiband network (MBN) system is needed to satisfy the stringent communication requirements. This trend triggers to utilize millimeter wave and THz frequency bands, in addition to traditional radio frequency band. In this paper, we divide the MBN control problem into two subproblems: the base station (BS) association problem and spectrum allocation problem. To jointly optimize these problems, we mainly focus on the cooperative game theory. According to the coalition formation game, each device considers the characteristics of different spectrum bands and forms its BS association for communication services. And then, a new control paradigm, called Max-min Multicriteria Bargaining Solution (MMBS), is introduced to solve the MBN spectrum allocation problem. By considering multiple criteria, the main concept of MMBS is the max–min–max optimization method based on the Nash product. By using the interactive relationship between BSs and individual devices, our joint control approach can effectively handle the MBN technology to ensure mutual advantages. Finally, simulation results show the efficiency and the effectiveness of our cooperative game approach. Compared with the existing MBN protocols, analytical results demonstrate the superior performance of the proposed solution.