Can my husband stay with me during the exam?

Yes, just ask. It is often allowable to have someone in the exam room if you so choose. Many men and women don't feel comfortable during a private-are examination on their partner/spouse and so they step out, but if you are ok with it and he has no trouble staying, just let doc know so. Good luck.
What exam? You should speak with your doctor about this, or his (or her) office staff. Most of the time, doctors are happy to have a support person in the room with a patient. Good luck.