Integrating massive multiple-input multiple-output (MIMO) into satellite network is regarded as an effective strategy to improve the spectral efficiency as well as the coverage of satellite communication. However, the inevitable intra-system and inter-system interference deteriorate the total performance of system. In this paper, we consider precoding in the 5G Satellite Integrated Network (5GSIN) with the deployment of Massive MIMO and propagation of shared millimeter-wave (mmWave) link. Taking the requirements of both frequency efficiency and energy assumption into account, a hybrid analog and digital pre-coding scheme in the specific scenario of 5GSIN is proposed. We model sum rate maximization problem for both of satellite and terrestrial system that incorporates maximum power constrains and minimum achievable rate requirements and formulate to a convex power allocation problem with Minimum Mean Square Error (MMSE) norm and Logarithmic Linearization method. In order to balance between performance and complexity, we propose an analog and digital separated hybrid precoding algorithm to mitigate intra-system interference. Moreover, an iterative power allocation with interference mitigation algorithm is also devised to mitigate interference from satellite to terrestrial link so that power allocation can be executed by generalized iterative algorithm. Simulation results show that our proposed hybrid precoding algorithm in 5GSIN can improve the overall spectral efficiency with a small amount of iterations.