The Bible states that a woman should obey her husband, but what if he is not a Christian husband? He believes in Jesus, God and the Holy Spirit, but he does not set forth a Christian lifestyle. I know a woman can still be religious on her own and believe in the Lord and practice her own lifestyle choices.
"Wives, submit to your own husbands, as is fitting in the Lord" (Colossians 3:18).
Nowhere in the commands for women to submit to their husbands is a qualification that it only needs to be done if the husband is a faithful Christian. The basis of the command originates in the Garden of Eden. After Adam and Eve's sin, "To the woman He said: "I will greatly multiply your sorrow and your conception; In pain you shall bring forth children; Your desire shall be for your husband, And he shall rule over you"" (Genesis 3:16). Discomfort in pregnancy and pain in labor do not only afflict Christian women with Christian husbands, so why conclude that "he shall rule over you" only applies to Christians married to Christians?
The idea of authority is that there is a hierarchy of command. "But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God" (I Corinthians 11:3). Whether a person wishes to recognize the chain of command or not, it still exists. Every person is under the authority of Christ. "For "He has put all things under His feet." But when He says "all things are put under Him," it is evident that He who put all things under Him is excepted" (I Corinthians 15:27). The only one not under Christ is the Father who placed the Son in his position.
Therefore, women are under the authority of men, whether they wish to recognize it or not. Men are under the authority of Christ whether they wish to recognize it or not. If a husband demands his wife do something that violates the commands of Christ, then the wife is required to obey the higher authority.
We can see this illustrated in government. All government exists by the will of God. "Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves" (Romans 13:1-2). But when the Jewish government demanded that the apostles stop preaching in the name of Jesus, the apostles' answer was, "We ought to obey God rather than men" (Acts 5:29). Where they could, the apostles obeyed the government, but when the government went outside its bound of authority by going against its head, the apostles rightly refused to follow.
The same would be true for a wife in submitting to her husband.