RATIONALE: Drugs used in chemotherapy, such as pemetrexed disodium, gemcitabine, and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) may kill more tumor cells. It is not yet known whether giving pemetrexed disodium with gemcitabine is more effective than giving pemetrexed disodium with carboplatin in treating malignant pleural mesothelioma. PURPOSE: This randomized phase II trial is studying pemetrexed disodium with gemcitabine and pemetrexed disodium with carboplatin to see how well the combinations work compared to historical controls in treating patients with advanced malignant pleural mesothelioma.