Did your husband fail to appear, fail to pay fine or have a warrant?
Are you familiar with how to find a DUI defense lawyer in LA?
Have you spoke with Immigration? If so, what exactly was said, please?
What is your husband's current status, LPR or "Green Card Holder," TPS, or no status?
What will happen to your husband depends on what his status is. Is he already in removal proceedings? If so, then he will have been served with a Notice To Appear (NTA) which will list the charges against him in the Immigration Court proceedings.
You need to consult with an Immigration Attorney as soon as possible so that you will know what you can do to prevent your husband from being deported as Immigration Court is a completely different and separate matter from the criminal court.