Any number of possibilities. He may have been married prior to entering service and the family - for whatever their reasons - didn't approve. There would be a civil record but you'd have to determine where the the marriage took place. The military would have a record ONLY if he had declared such status upon entering service and if he had been sending her an allotment. These records are very difficult to access.
He may have married overseas. There would be a civil record in the jurisdiction where the marriage was performed but, again, the trick is locating that jurisdiction. The military discouraged marriages between U. S. personnel and locals. Permission was required and the process for securing permission was made as difficult as possible. Many married anyway but the only way there would be an official (U. S.) record is if the indivdual had official permission.
Another possibility is that the discharge papers are in error (which happened a lot). I can track it down for you but I would have to charge you more than it would be worth (and probably more than you would be willing - or able - to pay). Probably best to leave it alone.