Human demonstrations provide a scalable source of diverse manipulation data, but leveraging them for robot learning remains challenging due to differences in embodiment, viewpoint, action spaces, and temporal structure. We introduce BATCH, a cross-embodiment learning framework that explicitly aligns human and robot behaviors. BATCH learns self-supervised temporal representations with a cycle-consistency objective to establish cross-embodiment correspondences without manual annotation. We further introduce two complementary training objectives that leverage these correspondences within an autoregressive videoaction diffusion model: behavior-aligned co-training and human-to-robot style transfer. On real-world manipulation tasks, BATCH improves generalization to unseen task configurations compared with training on unaligned data and prior cross-embodiment baselines, with additional gains from the style-transfer objective. Our results demonstrate that explicit behavior alignment enables more effective transfer from human demonstrations to robot policies.