The transition to Terahertz (THz) frequencies, providing an ultra-wide bandwidth, is a key driver for future wireless communication networks. However, the specific properties of the THz channel, such as severe path loss and vulnerability to blockage, pose a significant challenge in balancing data rate and reliability. This work considers reconfigurable intelligent surface (RIS)-aided THz communication, where the effective exploitation of a strong, but intermittent line-of-sight (LOS) path versus a reliable, yet weaker RIS-path is studied. We introduce a mixed-criticality superposition coding scheme that addresses this tradeoff from a data significance perspective. The results show that the proposed scheme enables reliable transmission for a portion of high-criticality data without significantly impacting the overall achievable sum rate and queuing delay. Additionally, we gain insights into how the LOS blockage probability and the channel gain of the RIS-link influence the rate performance of our scheme.