The　number　of　mitotic　cells　present　in　histopathological　slides　is　an　important　predictor　of　tumor　proliferation　in　the　diagnosis　of　breast　cancer.　However,　the　current　approaches　can　hardly　perform　precise　pixel-level　prediction　for　mitosis　datasets　with　only　weak　labels　(i.e.,　only　provide　the　centroid　location　of　mitotic　cells),　and　take　no　account　of　the　large　domain　gap　across　histopathological　slides　from　different　pathology　laboratories.　In　this　work,　we　propose　a　Domain　adaptive　Box-supervised　Instance　segmentation　Network　(DBIN)　to　address　the　above　issues.　In　DBIN,　we　propose　a　high-performance　Box-supervised　Instance-Aware　(BIA)　head　with　the　core　idea　of　redesigning　three　box-supervised　mask　loss　terms.　Furthermore,　we　add　a　Pseudo-Mask-supervised　Semantic　(PMS)　head　for　enriching　characteristics　extracted　from　underlying　feature　maps.　Besides,　we　align　the　pixel-level　feature　distributions　between　source　and　target　domains　by　a　Cross-Domain　Adaptive　Module　(CDAM),　so　as　to　adapt　the　detector　learned　from　one　lab　can　work　well　on　unlabeled　data　from　another　lab.　The　proposed　method　achieves　state-of-the-art　performance　across　four　mainstream　datasets.　A　series　of　analysis　and　experiments　show　that　our　proposed　BIA　and　PMS　head　can　accomplish　mitosis　pixel-wise　localization　under　weak　supervision,　and　we　can　boost　the　generalization　ability　of　our　model　by　CDAM.