No, it's not okay. If you are married, you cannot file as single. You have to file as either married filing jointly, together with your spouse, or as married filing separately. If you file jointly, in most cases it would not be legal for your parents to claim you as a dependent.
You seem to be saying that your parents don't know you are married. It's going to be hard to keep that secret for very long, but that's not a tax problem and I can't advise you about how to handle it. They won't necessarily find out because of your tax return, but they might, or it might come out some other way.
You haven't provided anywhere near enough details to determine whether your parents can still claim you as a dependent, but it's rare that a married person can be claimed by his or her parents. One thing that's certain, though, is that if your father is filing your tax return showing you as single, that's not a valid tax return. So your tax return is definitely wrong, and your parents' tax return might be wrong.
