Abstract: ‍ ‍Combining the satellite and aerial networks， the integrated satellite and aerial network with the advantages of wide coverage， large communication capacity， convenient and fast networking has shown a broad application prospect in the field of sixth generation mobile communication. At the same time， using terahertz frequency band for wireless transmission is considered to be an effective means to solve the problems of low spectrum efficiency and limited system capacity in the current wireless communication field. In this paper， a multi-objective beamforming scheme is proposed to support heterogeneous service in Terahertz integrated satellite and aerial networks. Specifically， the satellite network shares the spectrum resources with the aerial network and adopts multicast technique to serve satellite users， while the aerial network offers services to multiple aerial users through layer division multiplexing. Under this setup， we first formulate a multi-objective optimization problem （MOOP） to achieve a good trade-off between sum rate maximization and total transmit power minimization under the constraints of the users’ quality of service， satellite and UAV transmit power budgets. Then， we exploit the weighted Tchebycheff approach to transform the complicated MOOP into a single-objective problem. Furthermore， an iterative algorithm based on concave-convex process is proposed to deal with non-convex constraints， and the Pareto optimal solution is obtained. Finally， computer simulation verifies that the proposed algorithm can effectively improve the spectrum efficiency of the system by using layer division multiplexing technology， thus proving the superiority of the proposed algorithm.