Is money earned from working in a radio program funded by an interest-based bank unlawful money, and what should a worker do in this situation?

The fact that a usurious bank sponsors and funds the program does not affect the lawfulness of your work, as long as the program itself is not forbidden. Thus, there is no blame upon you for the aforementioned work. However, if a program is known to be forbidden because it promotes evil, calls to it, or includes it, then assisting in it is not permissible, due to the Almighty's saying: "And do not cooperate in sin and aggression."