Yes , it is possible to be discharged.However, I have handled several DUI cases with members of the armed forces and have never seen that form of punishment.Normally, I have seen the loss of post driving privileges, reduction in pay,transfer of duty,and loss of promotion.Please consult with your attorney before making a plea.
Rob answered the question in general, but I would add this... not enough information to give too much career advice. I did 20 years in the Army before law school and each branch handles DUIs differently. If you are an Officer or NCO, your chance of getting the boot eventually is greater.
If the chain of command doesn’t know, then you are in better shape. The fact that we are in two wars helps out a lot, but once peacetime kicks in, if the arrest made it in your record, you could get the boot after too many years down the road and wished you had jumped ship earlier. If you want to contact my office by phone, I will be glad to talk to you and give you my best advice after 20 years active duty and being a First Sergeant. Good Luck