My first year with ProSeries, I had the same issue. I did not set up any passwords and eventually I reached technical support and after many attempts, including directly accessing my computer remotely, the problem was fixed. Since you are both new, it could be part the initial set-up of your software. They had to use a master password from Intuit and some routine involving ALT, F12,C. This was 6 years ago so don't try this yourself, get on the hold list for technical support and keep at it till you get results.
It took me hours, so don't get too discouraged on the first day.
Have used for 20 years, never had a problem. I don't have the passwords option in Options. Cant efile anything.
If you go to Tools/Options/passwords....at bottom there is a checkbox "proseries should always prompt.....". Is that box checked by chance?