The Ethernet passive optical network is being regarded as one of the best solutions for next-generation optical access solutions. In time-division multiplexing–passive optical network technology (TDM–PON), the dynamic bandwidth allocation (DBA) plays a crucial role in efficiently and fairly allocating the bandwidth between all users. Moreover, the quality of service (QoS) is also an essential requirement to support triple-play services. However, many proposed DBA mechanisms are still unable to solve the idle period problem and enhance the differentiated services (DiffServ), which will decrease the quality of overall system performance. Therefore, this paper proposes a generic QoS-aware interleaved dynamic bandwidth allocation (QA-IDBA). The QA-IDBA can operate adaptively bi-partitioned interleaved scheduling with QoS-based predictive limit bandwidth allocation (QP-LBA) and excess bandwidth reallocation (EBR) with the remaining bandwidth compensation scheme to eliminate the idle period, enhance QoS, and effectively reduce high-priority traffic delay and jitter. We conduct detailed simulation experiments with 16 and 32 optical network units (ONUs) to show the scalability. Simulation results show that our proposed algorithms can accommodate the growth of ONUs and achieve better overall quality of system performance even if the high-priority traffic is increasing from 20%, 40%, and 60%.