You have a few options with a pending Application for Naturalization:
Your husband can withdraw the application "without prejudice" to refile at a later time.
Or he can proceed with the application; the application will not be approved for US citizensip while the criminal case remains pending. Depending on how long the criminal case takes to bring to completion, the naturalization application will continue on normal course until interview and from there may be continued awaiting the outcome of the criminal charges.
Criminal defense counsel must work with immigration counsel to minimize the chances of rendering your husband deportable.
Applicants are required to provide four documents in connection with a criminal charge:
A conviction will result in a denial and could result in your husband being rendered deportable. He should be represented in his naturalization application if he wants to proceed with it. It is important that even if the charges are dropped/dismissed, he is represented in his naturalization interview (now or future) so that he does not make "admissions in his own interest" that could constitute an admission of committing a crime.
Feel free to schedule a free 30 minute consultation with me to explain further.