Patients receive trastuzumab intravenously (IV) over 30-90 minutes on days 1 and 8 and aldesleukin subcutaneously (SC) on days 2-7 and 9-21. Beginning on day 22, patients receive trastuzumab IV over 30 minutes every 14 days. Patients also receive aldesleukin SC daily on days 1-14. Treatment continues for 1 year in the absence of disease progression or unacceptable toxicity.