Being in a marriage when your husband won't repent of his sin doesn't mean you can't glorify God. It doesn't mean your life has to be miserable, or that you are doomed or stuck. Your circumstances may be quite difficult and challenging, but with God's help you can still find joy and fulfillment in your marriage.
You must remember that God is fully aware of your situation. Marriage relationships are very important to God because they picture the relationship He has with the church (Eph. 5). He has a vested interest in your marriage and in you and your husband. God desires all men everywhere to repent and bring Him glory and honor.
If you husband is living in unrepentant sin, I want you to begin praying for him. Ask the Lord to begin to work in his heart, to see his sin, and to give him the desire to repent. Pray for yourself, that you will not become bitter and angry through this process as you wait for your husband's repentance.
Get the plank out of your own eye. What would your husband say is your problem? Take responsibility for your sin, not so you can be self-righteous before him but so you can honor God.
Biblically reprove your husband (Matt. 18:15). Your goal is to help your husband see he is living a sinful life pattern and needs to repent. You must be gentle, loving, and honest, having no fear as you confront him (2 Tim 1:7).
Get your church involved. One of the blessings of church membership is accountability! When you belong to a church body rather than just attend the church there are others who can help you and your husband grow and change. They will encourage you when it's needed, and they will also hold you accountable for your actions. The process outlined in Matthew 18:15-18 is sometimes wrongly misunderstood to be punishment with the goal to remove a person from church. In reality, this passage is intended to guide the church in restoring those who fall into sin (Gal. 6:1) and need help. The goal is always repentance and restoration.
As you go through this time you will need accountability or biblical counseling and discipleship for yourself. You will need encouragement to overcome evil with good (Rom. 12:17), and to learn how to respond biblically to your husband's actions and attitudes. There may be times you wonder how you can continue to live in the circumstances and you may become weary and discouraged. Having a solid discipleship relationship will help you to persevere (1 Cor. 10:13) and keep your thoughts, beliefs, and desires focused on glorifying God.
There are times God allows consequences that affect your whole family for the purpose of moving your husband to repent. Affliction and suffering are never easy, even in the best of marriages. I would encourage you to memorize a passage such as Isaiah 40:28-31. You can recall these words when you think you cannot go on.
You must realize your husband may never change. That sounds pretty depressing, but you would be wise to accept that possibility. While God desires your husband come to repentance, He will not force him. You can do it all "right" and yet your husband may not change. You may have to remind yourself frequently that biblical change is less about you and more about your husband and his relationship to God.
As your relationship with the Lord deepens you will find the strength to live with your husband just as he is and you will experience comfort, and fulfillment as you seek to honor God in the midst of your marriage.