This paper reviews the state-of-the art technologies and techniques for integrating satellite and terrestrial networks within a 5G and Beyond Networks (5GBYNs). It highlights key limitations in existing architectures, particularly in addressing interoperability, resilience, and Quality of Service (QoS) for real-time applications. In response, this work proposes a novel Software-Defined Networking (SDN)-based framework for reliable satellite–terrestrial integration. The proposed framework leverages intelligent traffic steering and dynamic access network selection to optimise real-time communications. By addressing gaps in the literature with a distributed SDN control approach spanning terrestrial and space domains, the framework enhances resilience against disruptions, such as natural disasters, while maintaining low latency and jitter. Future research directions are outlined to refine the design and explore its application in 6G systems.