Trastuzumab in Treating Patients With Locally Advanced or Metastatic Gallbladder Cancer or Bile Duct Cancer That Cannot Be Removed by Surgery

Criteria: * Adenocarcinoma of the gallbladder * Recurrent extrahepatic bile duct cancer * Recurrent gallbladder cancer * Unresectable extrahepatic bile duct cancer * Adenocarcinoma of the extrahepatic bile duct * Unresectable gallbladder cancer * Prior surgery and radiotherapy allowed * At least 28 days since prior chemotherapy (6 weeks for nitrosoureas and mitomycin C) and recovered * No other concurrent investigational agents, chemotherapy, radiotherapy, or hormonal therapy * Concurrent hormones administered for nondisease-related conditions (e.g., insulin for diabetes) allowed * No concurrent corticosteroids or anticonvulsants * Concurrent steroids administered for antiemesis, adrenal failure, or septic shock allowed * No concurrent combination antiretroviral therapy for HIV-positive patients * Histologically or cytologically confirmed adenocarcinoma of the gallbladder or bile duct, meeting all of the following criteria: locally advanced or metastatic disease that is unresectable * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques or \>= 10 mm by spiral computed tomography (CT) scan * Tumor that recurs within a previously irradiated field is considered measurable disease if recurrence is documented and measurable by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Tumor must be Her2/neu positive by Fluorescence in situ hybridization (FISH)testing * No symptomatic brain metastases * The Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 OR Karnofsky PS 60-100% * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Fertile patients must use effective contraception prior to, during, and for \>= 3 months after completion of study treatment * Creatinine =\< 2 times upper limits of normal (ULN) OR creatinine clearance \>= 60 mL/min * No other active malignancy * Left Ventricular Ejection Fraction (LVEF) \>= 50% * No concurrent uncontrolled illness * No ongoing or active infection requiring systemic IV antibiotics on day 1 of treatment * No symptomatic New York Heart Association class III-IV congestive heart failure * No unstable angina pectoris * No unstable cardiac arrhythmia requiring medication * No more than 1 prior systemic chemotherapy regimen * White Blood Count (WBC) \>= 3,000/mm\^3 * Platelet count \>= 40,000/mm\^3 * Bilirubin =\< 4 mg/dL * Aspartate aminotransferase and alanine aminotransferase (AST and ALT) =\< 5 times upper limit of normal (ULN) * Not pregnant or nursing * Negative pregnancy test