This paper investigates a satellite-terrestrial backhaul framework to enhance efficient data offloading for heterogeneous terminals, including delay-sensitive and delay-tolerant users. In the considered architecture, ground terminals in satellite-terrestrial small cells can access different services via the satelliteterrestrial station (STS) in each cell. The satellite offloads the requested services to corresponding STSs, and each STS provides services to terrestrial terminals via an OFDM-based downlink system. We aim to maximize the sum throughput of all small cells while integrating joint satellite backhaul power allocation and STS downlink resource allocation. The problem is firstly decomposed into two types of subproblems by decoupling the optimization of satellite backhaul capacity and downlink capacity in small cells. Then, to satisfy users' delay requirements, the downlink STS throughput is maximized over multiple slots, and we propose a two-step algorithm to schedule users during these slots. By taking advantage of a delayviolation parameter, the algorithm iteratively approaches the optimal power and subchannel solution, while guaranteeing the delay requirements. Moreover, to reduce the computational complexity, we propose a greedy-based sub-optimal scheduling algorithm where delay requirements are guaranteed by users' selfsearch for favorable resources, aiming at sacrificing the minimum throughput in exchange for the delay performance. Simulation results show our algorithms effectively improve the throughput performance while ensuring the delay constraints, maintaining a well-performed balance between throughput and delay performance. INDEX TERMS Satellite-terrestrial backhauling, heterogenous services, small cells, delay awareness, lowcomplexity, power allocation, subchannel allocation.