Terahertz (THz) communication offers the necessary bandwidth to meet the high data rate demands of next-generation wireless systems. However, it faces significant challenges, including severe path loss, dynamic blockages, and beam misalignment, which jeopardize communication reliability. Given that many 6G use cases require both high data rates and strong reliability, robust transmission schemes that achieve high throughput under these challenging conditions are essential for the effective use of high-frequency bands. In this context, we propose a novel mixed-criticality superposition coding scheme for reconfigurable intelligent surface (RIS)-assisted THz systems. This scheme leverages both the strong but intermittent direct line-of-sight link and the more reliable, yet weaker, RIS path to ensure robust delivery of high-criticality data while maintaining high overall throughput. We model a mixed-criticality queuing system and optimize transmit power to meet reliability and queue stability constraints. Simulation results show that our approach significantly reduces queuing delays for critical data while sustaining high overall throughput, outperforming conventional time-sharing methods. Additionally, we examine the impact of blockage, beam misalignment, and beamwidth adaptation on system performance. These results demonstrate that our scheme effectively balances reliability and throughput under challenging conditions, while also underscoring the need for robust beamforming techniques to mitigate the impact of misalignment in RIS-assisted channels.