I switch back to IE load the bank's software/billpay. It doesn't "answer" mozzila's replies properly.
If it were me, I'd bitch to the site programmers to fix their nonstandard, possibly insecure, code.
There is a Firefox extension called "ieview" at http://ieview.mozdev.org/ which solved this problem for me. Lets you shell out to IE to re-load the currently browsed site and drop right back to Firefox when finished.