Since Islam is against an interest based economy, is it permissable for a Muslim to work for a bank?

The question is not one that can be easily answered by yes or no. It depends on an individual's own conscience to establish whether there own involvement within a job they do is unlawful Islamically or harmful to others. Interest permeats our society and its dealings to such a degree that there are no safe havens. This does not just apply to banks. Our money supply comes into circulation as an interest-bearing debt, so anybody using money will have some indirect involvement with interest. The problem, therefore, cannot be resolved on an individual level, but requires political pressure and action.