Praise be to Allah.
Firstly, we advise this husband to repent to Allaah from drinking alcohol, because drinking alcohol is haraam according to the Book of Allaah, the Sunnah of His Messenger (peace and blessings of Allaah be upon him) and the consensus of the Muslims. Allaah says (interpretation of the meaning):
“O you who believe! Intoxicants (all kinds of alcoholic drinks), and gambling, and Al Ansaab [stone altars for offering sacrifices to idols etc.], and Al Azlaam (arrows for seeking luck or decision) are an abomination of Shaytaan’s (Satan’s) handiwork. So avoid (strictly all) that (abomination) in order that you may be successful.
Shaytaan (Satan) wants only to excite enmity and hatred between you with intoxicants (alcoholic drinks) and gambling, and hinder you from the remembrance of Allaah and from As‑Salaah (the prayer). So, will you not then abstain?
And obey Allaah and the Messenger (Muhammad), and beware (of even coming near to drinking or gambling or Al‑Ansaab, or Al‑Azlaam) and fear Allaah. Then if you turn away, you should know that it is Our Messenger’s duty to convey (the Message) in the clearest way” [al-Maa'idah 5:90-92]
It was narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Every intoxicant is liquor and every liquor is haraam.” (Narrated by Muslim, al-Ashribah 3735)
The scholars are unanimously agreed, with no dispute on this matter. Some of the scholars even considered the prohibition of alcohol to be one of the most well known teachings of Islam (ignorance of which is inexcusable). So our advice to him is that he should give up drinking alcohol, and be content with [?] that which Allaah has permitted to him of good drinks, and not seek that which Allaah has forbidden. Alcohol is the mother of evil and the key to all evil. Allaah has issued a stern warning to those who drink it and do not repent from that. It was narrated from Jaabir that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Allaah has made a covenant to those who drink alcohol, that He will make them drink teenat al-khabaal.” They said, “O Messenger of Allaah, what is teenat al-khabaal?” He said, “The sweat of the people of Hell,” or, “The juice of the people of Hell.” (Narrated by Muslim, al-Ashribah, 3732)
It is easy to give it up if one is sincere and determined, and seeks the help of Allaah, may He be exalted.
With regard to yourself, there is no sin on you if your husband drinks alcohol, because a person will not be brought to account for the sins of another. Allaah says (interpretation of the meaning):
“And no bearer of burdens shall bear another’s burden”[Faatir 35:18]
Rather, you will be rewarded for your sincere advice to your husband. Your living with him is not haraam, because drinking alcohol does not make him a kaafir. So keep on calling him, advising him and making du’aa’ for him, and may Allaah cause him to repent. If your keeping away from him in bed will serve the purpose of deterring him and making give up alcohol, then it is permissible, but if it will not achieve anything, then do not do it. We ask Allaah to guide us all and give us strength. For more information see the fatwa of Shaykh Ibn ‘Uthaymeen, 2/890