If my husband was charged of domestic abused and now he was applying for his citizenship, what will happen?

A full legal analysis about your husband's eligibility for naturalization will depend upon the outcome of the criminal charges. Domestic violence indeed can stand in the way of naturalization eligibility and it even can have more harsh immigration-related consequences. It would have been wise to have engaged an immigration attorney at the time your husband first was arrested and also at the time your husband applied to become a naturalized citizen, so that the issue could be fully addressed at that point or points. Note that some criminal case dispositions that are not convictions in the criminal legal context still can be treated as convictions by the USCIS - that often turns on whether a defendant has admitted to the elements of the offense in connection with pretrial diversion or a similar disposition. There really is no substitute for consulting with an immigration attorney now. After learning all of the relevant information and seeing the court-certified disposition documents, an immigration attorney could advise about eligibility and about steps to take at this point - and that is true regardless of whether the criminal case already has been concluded.