It's safest to assume your employer can see everything. Now if the sites you visit are all property secured your employer probably won't be eavesdropping passwords,1 but that data could still be in your browser. This site isn't the place for a technical analysis; instead let's focus on the human element. Have you ever forgotten to clear a session? Have you ever let your browser remember an "unimportant" password? Even the most careful humans goof sometimes, and when they do, anybody with access to the machine can use your stored credentials.
All that said, your IT department probably doesn't care. You probably face a bigger risk from other users of your computer -- you're probably not perfect at locking when you step away, right? Or you might allow a coworker to debug something in your environment. Or you might get a new machine and hand the old one off to an intern without reimaging.
The chance of having your private data compromised is very small in most workplaces, but it is not zero. If checking your bank balance from work is that important, you might decide it's fine. On the other hand, you could wait until you get home, or use your phone.
Finally, you should assume that your non-private browsing activity is all logged -- URLs, timestamps, and maybe other stuff. IT departments do look at this information sometimes -- usually in the aggregate, but if they see something interesting they might drill down.
1 There are things they could do to eavesdrop on secure connections, but it would be an intentional move. The tools normally used by a non-evil corporate IT department are unlikely to compromise your passwords for secure sites. But nothing is ever guaranteed.