This study addresses the Domain-Class Incremental Learning problem, a realistic but challenging continual learning scenario where both the domain distribution and target classes vary across tasks. To handle these diverse tasks, pre-trained Vision-Language Models (VLMs) are introduced for their strong generalizability. However, this incurs a new problem: the knowledge encoded in the pre-trained VLMs may be disturbed when adapting to new tasks, compromising their inherent zero-shot ability. Existing methods tackle it by tuning VLMs with knowledge distillation on extra datasets, which demands heavy computation overhead. To address this problem efficiently, we propose the Distribution-aware Interference-free Knowledge Integration (DIKI) framework, retaining pre-trained knowledge of VLMs from a perspective of avoiding information interference. Specifically, we design a fully residual mechanism to infuse newly learned knowledge into a frozen backbone, while introducing minimal adverse impacts on pre-trained knowledge. Besides, this residual property enables our distribution-aware integration calibration scheme, explicitly controlling the information implantation process for test data from unseen distributions. Experiments demonstrate that our DIKI surpasses the current state-of-the-art approach using only 0.86% of the trained parameters and requiring substantially less training time.