In this paper, we introduce a novel framework consisting of hybrid bit-level and generative semantic communications for efficient downlink image transmission within space-air-ground integrated networks (SAGINs). The proposed model comprises multiple low Earth orbit (LEO) satellites, unmanned aerial vehicles (UAVs), and ground users. Considering the limitations in signal coverage and receiver antennas that make the direct communication between satellites and ground users unfeasible in many scenarios, thus UAVs serve as relays and forward images from satellites to the ground users. Our hybrid communication framework effectively combines bit-level transmission with several semantic-level image generation modes, optimizing bandwidth usage to meet stringent satellite link budget constraints and ensure communication reliability and low latency under low signal-to-noise ratio (SNR) conditions. To reduce the transmission delay while ensuring reconstruction quality for the ground user, we propose a novel metric to measure delay and reconstruction quality in the proposed system, and employ a deep reinforcement learning (DRL)-based strategy to optimize resource allocation in the proposed network. Simulation results demonstrate the superiority of the proposed framework in terms of communication resource conservation, reduced latency, and maintaining high image quality, significantly outperforming traditional solutions. Therefore, the proposed framework can ensure that real-time image transmission requirements in SAGINs, even under dynamic network conditions and user demand.