Combination Chemotherapy With or Without Bevacizumab in Treating Patients With Malignant Mesothelioma

Inclusion Criteria: * Histologically or cytologically confirmed malignant pleural or peritoneal mesothelioma that is not amenable to curative surgery * Epithelial, sarcomatoid, or mixed subtype * Evidence of gross unresectability, including, but not limited to, the following conditions: * Direct extension into the chest wall * Mediastinal or hilar lymphadenopathy * Pulmonary or cardiac function that is inadequate to tolerate resection * Sarcomatoid or mixed histology * Pleural mesothelioma must be stage II or greater using the International Mesothelioma Interest Group staging system * Measurable disease outside prior irradiation port * At least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan * Pleural effusions and ascites are not considered measurable lesions * Site in pleura, lung, liver, or retroperitoneum that can be assessed by MRI for evaluation of blood flow * No obvious tumor involvement of major vessels by CT scan * No known brain metastases * Performance status - ECOG 0-1 * More than 3 months * WBC at least 3,000/mm\^3 * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * No history of bleeding diathesis * Bilirubin normal * AST/ALT no greater than 2.5 times upper limit of normal * INR no greater than 1.5 * Creatinine no greater than 1.5 mg/dL * Creatinine clearance at least 60 mL/min * If 1+ or greater proteinuria on dipstick, then must have less than 500 mg of protein/24-hour urine collection * No significant renal impairment * See Disease Characteristics * No history deep vein thrombosis * No myocardial ischemia or infarction within the past 6 months * No uncompensated coronary artery disease within the past 6 months * No uncontrolled hypertension * No symptomatic congestive heart failure * No unstable angina pectoris within the past 6 months * No cardiac arrhythmia * No transient ischemic attack within the past 6 months * No cerebrovascular accident within the past 6 months * No other arterial thromboembolic event within the past 6 months * No clinically significant peripheral artery disease * See Disease Characteristics * No history of pulmonary embolism * No prior allergic reactions attributed to compounds of similar chemical or biologic composition to bevacizumab or other study agents * No other active malignancy within the past 5 years except nonmelanoma skin cancer or carcinoma in situ of the cervix * No ongoing or active infection * No other concurrent uncontrolled illness that would preclude study participation * No psychiatric illness or social situations that would preclude compliance * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No growth factors for 24 hours before, during, or for 24 hours after cytotoxic chemotherapy * See Biologic therapy * Prior intrapleural cytotoxic agents (including bleomycin) allowed * No prior systemic cytotoxic chemotherapy * See Disease Characteristics * At least 4 weeks since prior radiotherapy and recovered * See Disease Characteristics * At least 6 weeks since prior major surgery * At least 30 days since prior investigational drug * No other concurrent investigational or commercial agents or therapies * No concurrent combination antiretroviral therapy for HIV-positive patients