Language-conditioned manipulation facilitates human-robot interaction via behavioral cloning (BC), which learns control policies from human demonstrations and serves as a cornerstone of embodied AI. Overcoming compounding errors in sequential action decisions remains a central challenge to improving BC performance. Existing approaches mitigate compounding errors through data augmentation, expressive representation, or temporal abstraction. However, they suffer from physical discontinuities and semantic-physical misalignment, leading to inaccurate action cloning and intermittent execution. In this paper, we present Continuous vision-language-action Co-Learning with Semantic-Physical Alignment (CCoL), a novel BC framework that ensures temporally consistent execution and fine-grained semantic grounding. It generates robust and smooth action execution trajectories through continuous co-learning across vision, language, and proprioceptive inputs (e.g., robot internal states). Meanwhile, we anchor language semantics to visuomotor representations by a bidirectional cross-attention to learn contextual information for action generation, successfully overcoming the problem of semantic-physical misalignment. Extensive experiments show that CCoL achieves an average 8.0% relative improvement across three simulation suites, with up to 19.2% relative gain in human-demonstrated bimanual insertion tasks. Real-world tests on a 7-DoF robot further confirm CCoL's generalization under unseen and noisy object states.