Satellite communication networks with onboard processing (OBP) satellites can provide high-speed data transmission rates and global service coverage with reduced propagation delays. This article proposes a means of analyzing the quantitative reliability of the satellite communication network systems. First, we identify the four major factors that affect the quality of network services: the OBP states, uplink channels, downlink channels, and uplink packet collision losses. Based on these four factors, a Markov model is derived to analyze the probability distributions of various network states. Analytic results show the network reliability with respect to the OBP structures and space radiation environments. The relationship between network reliability and throughput according to the packet traffic load is also quantitatively analyzed. Finally, based on the developed model, a method is suggested for iteratively updating the reliability distribution of network systems affected by changes in the four factors as well as network access time changes. The numerical results show an indication of the satellite network reliability to provide references whether adjusted elements of the four factors are eligible to sustain reliable end-to-end services.