Successfully completed deferred adjudication cases are eligible for non-disclosure, not expunction. Your husband needs to file a petition for non-disclosure to limit public access to the record.
Your husband's case cannot be expunged because it was not dismissed nor did he get a not guilty after a trial. However, he can petition the court for nondisclosure of his record. If his case was a felony, he must wait 5 years after the probation is completed. The likelihood of nondisclosure being granted depends on what your husband does with his life in the interim.