Real-world lectures follow a predefined topic inventory (e.g., a syllabus), but instructors often reorder, paraphrase, or skip items, creating mismatches between the outline and the spoken content. Lectures also contain non-topical utterances (openings, transitions and wrap-ups) that should not be assigned to any topic, yet existing corpora rarely model both challenges. We present **MOSAIC** (**M**ultimodal **O**pen-course **S**egmentation and **A**lignment corpus **I**n **C**hinese), a large-scale Chinese MOOC corpus for *topic-guided segmentation and alignment* under predefined inventories, with explicit *non-topical* labels and matched slide resources. MOSAIC includes **MOSAIC-G** (human-annotated gold benchmark with utterance-level topic alignment and video-level links to matched slide resources) and **MOSAIC-S** (automatically labeled silver data), collectively covering 179 courses and 14,942 videos. To scale annotation, we propose **DORA** (**D**ual-stage **O**utline **R**efinement and **A**lignment), a two-stage pipeline that refines noisy inventories and then performs joint segmentation and topic assignment. Experiments show that silver supervision substantially improves the performance of local models and that incorporating slides consistently benefits knowledge-point extraction, a lecture-comprehension proxy.