Your first step is to ask your midwife or doctor if they know what the hospital policy is where you've chosen to give birth. You will want to verify their answer with the labor and delivery unit at the hospital. If there is an exception available, the hospital will be able to explain it to you.
If there is no exception, you will need to talk to someone about getting one if it is important to you to have your husband with you during the epidural administration. This might be the head of labor and delivery or you may need to go to the board of directors. This is not as difficult as it seems. It might also be as simple as the anesthesiologist on call making an exception. Talking to all of these groups before you have your baby is always best.
There are some hospitals that allow a doula to stay and not the spouse. This might be another alternative for you. This is particularly true if your husband or partner can't handle the epidural administration.
If someone stays with you, typically the can stay at your bedside. If you are receiving an epidural while lying down on your side, then can kneel next to the bed, hold your hand and talk to you without seeing anything. If you are sitting up, they may be able to stand in front of you, while you hold onto them for support. A doctor or nurse can show you which positions work best for support people.