How can my husband get an OTH discharge upgrade?

Yes. Generally, your husband might get that OTH changed to a General (under honorable conditions) or Honorable Discharge, depending on the merits of his specific case. Each individual branch of military service maintains boards that consider appeals of adminisrative separations. The Army offers the Discharge Review Board and Army Board for Correction of Military Records. You have the right to legal representation during both administrative procceses, but it is not required. An application for relief can result in his receiving a better discharge characterization, a change in his reenlistment code and/or a new narrative section on his DD-214. I recommend that you speak with legal counsel to explore these various options. Good luck!