The continuous progression of networking systems demands the deployment of adaptive and high-performance infrastructures to seamlessly support the requirements of future-generation networks. The upcoming generation of networks is expected to rely heavily on space-air-ground integrated networks (SAGINs). These next-generation (NG) networks provide global coverage, increased capacity, and minimized latency, effectively addressing connectivity issues in remote and underserved areas. The HAAPs operating in the stratosphere offer an effective solution to improve network coverage, capacity, and reliability. In addition to HAAPs, drones or UAVs have transformed various industries by providing a flexible and practical approach to surveillance, mapping, and data collection. An NG-SAGIN presents a distinctive mix of reconfigurability, elasticity, and robustness. However, ensuring the dependability of such networks is essential to maintain continuous connectivity and reliable services. This paper presents an in-depth examination of the dependability analysis of NG-SAGINs. A dependability framework is designed and analyzed through a semi-Markov modeling technique to derive the dependability parameters of an NG-SAGIN. The long-run results for the dependability parameters of NG-SAGINs are obtained analytically. Graphical representations are utilized to display the numerical outcomes, offering insights into how availability and reliability respond to variations in system parameters, with results clearly showing that both availability and reliability consistently decline as the failure rate increases.