Being the partner of an alcoholic, I have found, is difficult in a lot of ways because of all the secrets and the lies. It actually has made me crazy to take part in keeping secrets from the family members of the alcoholic. Some family will understand when u tell them, and some will not. Likely if they do, they are already in recovery. I have discussed alcoholism and addiction with family of my old ABFs. It is entirely up to you whether or not you tell AH's family the truth. You must follow your own conscience and your own heart. Understand, though, that you may not get the reaction you expect.
I personally informed my alcoholic and addicted XBF's family of his problems, because I felt it was my duty to let someone know how sick he is. Nobody died over my telling them, nobody got upset at me or harrassed me or anything. Trust your instincts and follow your heart I always say. It has never failed me.
Good luck.