For the multi-user scenarios of the high-altitude platform （HAP）-assisted integrated satellite and aerial network， this paper proposes a novel hybrid wireless transmission scheme on terahertz （THz） and millimeter-wave （mmWave） bands， aiming at providing reliable access for heterogeneous users and solving the problem of capacity constraints of the satellite backbone network. Firstly， according to the relevance and service priorities among users， terrestrial users are divided into two groups， each of which includes a primary user and a secondary user. The secondary user adopts the cognitive radio-based non-orthogonal multiple access （CR-NOMA） technique to control its transmit power without compromising the quality of service （QoS） of the primary user， while the inter-group interference is eliminated by the zero-forcing （ZF） based beamforming technique. Secondly， it is assumed that the channel from each user to HAP experiences mmWave band with Nakagami-m distribution， while the channel from HAP to satellite experiences THz band with α-μ distribution. The closed-form expressions of the users’ outage probability and the system throughput are derived with further consideration of the pointing error in the THz band. Finally， computer simulation verifies the correctness of the theoretical analysis and the superiority of the proposed scheme， and characterizes the impact of relevant parameters on the performance of each user and system， thus providing a useful reference for exploring future integrated satellite and aerial network enabled by THz and mmWave bands.