Deep learning-based semantic communication has largely relied on analog or semi-digital transmission, which limits compatibility with modern digital communication infrastructures. Recent studies have employed vector quantization (VQ) to enable discrete semantic transmission, yet existing methods neglect channel state information during codebook optimization, leading to suboptimal robustness. To bridge this gap, we propose a channel-aware vector quantization (CAVQ) algorithm within a joint source-channel coding (JSCC) framework, termed VQJSCC, established on a discrete memoryless channel. In this framework, semantic features are discretized and directly mapped to modulation constellation symbols, while CAVQ integrates channel transition probabilities into the quantization process, aligning easily confused symbols with semantically similar codewords. A multi-codebook alignment mechanism is further introduced to handle mismatches between codebook order and modulation order by decomposing the transmission stream into multiple independently optimized subchannels. Experimental results demonstrate that VQJSCC effectively mitigates the digital cliff effect, achieves superior reconstruction quality across various modulation schemes, and outperforms state-of-the-art digital semantic communication baselines in both robustness and efficiency.