RATIONALE: Drugs used in chemotherapy, such as doxorubicin, cyclophosphamide, and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as trastuzumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Lapatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving combination chemotherapy together with trastuzumab and lapatinib after surgery may kill any tumor cells that remain after surgery.