Purpose: The purposes of this study are to determine:

1. The safety of Pemetrexed plus Gemcitabine and any side effects that might be associated with the combination of these two drugs.
2. Whether Pemetrexed plus Gemcitabine can help patients with mesothelioma live longer.
3. Whether Pemetrexed plus Gemcitabine can make the tumor smaller or disappear, and for how long.
4. To see if patients feel better while taking Pemetrexed plus Gemcitabine.