These days, the term of Internet of Things (IoT) becomes popular to interact and cooperate with individual smart objects, and one of the most critical challenges for IoT is to achieve efficient resource sharing as well as ensure safetystringent timing constraints. To design such reliable real-time IoT, this paper focuses on the concept of mixed-criticality (MC) introduced to address the low processor utilization on traditional real-time systems. Although different worst-case execution time estimates depending on criticality are proven effective on processor scheduling, the MC concept is not yet mature on distributed systems (such as IoT), especially with end-to-end deadline guarantee. To the best of our knowledge, this paper presents the first attempt to apply the MC concept into interference (or jitter), which is a complicated source of pessimism when analyzing the schedulability of distributed systems. Our goal is to guarantee the end-to-end deadlines of high-criticality flows and minimize the deadline miss ratio of low-criticality flows in distributed systems. To achieve this goal, we introduce a jitter-based MC (JMC) scheduling framework, which supports node-level mode changes in distributed systems. We present an optimal feasibility condition (subject to given schedulability analysis) and two policies to determine jitter-threshold values to achieve the goal in different conditions. Via simulation results for randomly generated workloads, JMC outperforms an existing criticality-monotonic scheme in terms of achieving higher schedulability and fewer deadline misses.