Time-triggered automotive networks use time-triggered protocols (FlexRay, TTEthernet, etc.) for periodic message transmissions that often originate from safety and time-critical applications. One of the major challenges with time-triggered transmissions is jitter, which is the unpredictable delay-induced deviation from the actual periodicity of a message. Failure to account for jitter can be catastrophic in time-sensitive systems, such as automotive platforms. In this article, we propose a novel scheduling framework (JAMS-SG) that satisfies timing constraints during message delivery for both jitter-affected time-triggered messages and high-priority event-triggered messages in automotive networks. At design time, JAMS-SG performs jitter-aware frame packing (packing of multiple signals from Electronic Control Units (ECUs) into messages) and schedules synthesis with a hybrid heuristic. At runtime, a Multi-Level Feedback Queue (MLFQ) handles jitter-affected time-triggered messages and high-priority event-triggered messages that are scheduled using a runtime scheduler. Our simulation results, based on messages and network traffic data from a real vehicle, indicate that JAMS-SG is highly scalable and outperforms the best-known prior work in the area in the presence of jitter.