The space-air-ground integrated network (SAGIN) is a pivotal architecture to support ubiquitous connectivity in the upcoming 6G era. Inter-operator resource and service sharing is a promising way to realize such a huge network, utilizing resources efficiently and reducing construction costs. Given the rationality of operators, the configuration of resources and services in SAGIN should focus on both the overall system performance and individual benefits of operators. Motivated by emerging symbiotic communication facilitating mutual benefits across different radio systems, we investigate the resource and service sharing in SAGIN from a symbiotic communication perspective in this paper. In particular, we consider a SAGIN consisting of a ground network operator (GNO) and a satellite network operator (SNO). Specifically, we aim to maximize the weighted sum rate (WSR) of the whole SAGIN by jointly optimizing the user association, resource allocation, and beamforming. Besides, we introduce a sharing coefficient to characterize the revenue of operators. Operators may suffer revenue loss when only focusing on maximizing the WSR. In pursuit of mutual benefits, we propose a mutual benefit constraint (MBC) to ensure that each operator obtains revenue gains. Then, we develop a centralized algorithm based on the successive convex approximation (SCA) method. Considering that the centralized algorithm is difficult to implement, we propose a distributed algorithm based on Lagrangian dual decomposition and the consensus alternating direction method of multipliers (ADMM). Finally, we provide extensive numerical simulations to demonstrate the effectiveness of the two proposed algorithms, and the distributed optimization algorithm can approach the performance of the centralized one.