If your bank demands you use IE for online banking, then I would be calling their IT departments as well as their security departments and demand they change. Either that or switch to a bank that doesn’t lock you into using insecure and dangerous products. (For example, Wells Fargo’s online banking system works flawlessly with Mozilla.)
And if you’re still using IE, why?
UPDATE: The Houston Chronicle agrees.
UPDATE: So does eWeek
UPDATE: …and so does Business Week