The Judgment of Dismissal means that the case is no longer pending and that he was not convicted of the crime. If someone were to look at his criminal history it would show that he was arrested for the original crime but that it was dismissed after he successfully completed the DVDS program. In order for there to be no record of the event, he would need to file to have the arrest expunged. Most DVDS programs have a clause in the agreement that says you won't file to have the arrest expunged for a certain amount of time, so look at the original agreement if you still have it. Either way, a criminal law attorney should be able to help you with that.
It is best to consult privately with an immigration attorney for any immigration questions. Typically immigration frowns upon any acts of domestic violence, but it's best to speak to an immigration attorney regarding his specific case. The answer will depend on his current immigration status.
If the case has need dismissed, your husband must file to have the arrest record and court documents sealed and expunged from the system. He can then legally say that he was not arrested for that event. For most purposes it is as if it never occurred.
You should consult a lawyer about the correct way to file a motion to seal the arrest record.
This response should not be relied upon as advice. Communication in this forum does not create an attorney client relationship.