Some men simply refuse to lead no matter what opportunity is presented to them. Often they are unbelieving men who married unbelieving women who have since converted.
In such cases, my counsel to the women is to have as reasonable a discussion as possible with their husband on this topic. When presented with facts, an unbelieving husband may agree to relieve his wife of some of the responsibilities in the home and for the family.
If the husband is a believer and still chooses to abdicate his responsibility it does not change the fact that God has placed him in charge and he is in charge. You must obey God first, and that means you treat your husband as the leader he is.
This does not mean you constantly nag him and remind him that he is the leader, it means you simply subjugate yourself to the second chair, and defer to him in matters of leadership.
For example: A wife who patiently explains that the children are disrespecting her, and that she sees a need for a fatherly influence may win him over to take a more active role in disciplining the children. But a word of caution is needed her ladies; if you are set on having your husband lead, you must stay out of the way and let him do it! Many a man has come to a counseling session complaining that his wife begged and nagged at him to take more of a role in the disciplining of the children only to criticize him and step in to reverse his decisions when he did something she did not like. If you do this I promise you, he will stop participating and you will have little to no hope of him trying again.
Some husbands are not interested in watching over the finances of the home, they prefer to have their wives do it. It may be that you are better with figures than he is and if this is something he wishes for you to take care of, there is no harm in doing it providing he is involved every step of the way. For example, telling him that a certain number of bills need to be paid and how much the total will be is important. Asking him if he wishes for you to overpay or pay only a minimum is also important. Consulting with him before you purchase something for you or the kids, especially if it is an unplanned purchase or an extra item is also a way of recognizing his headship over your family.
Demonstrating this to your children will send a loud and clear message to them that dad is in charge even if he doesn't want to be, because God says he is in charge.
There seems to be a rather large contingent of men who leave all the outdoor yard work to their wives. Not because the wives likes it, but because the men simply won't do it. Gardening is one thing, mowing and shoveling, and heavier work are quite another. I know, some of you enjoy that kind of thing and if you do, that is fine. However, I think we must keep the Scriptural principles in mind when approaching some of these chores. Is is loving for a man to sit inside watching sports while his wife mows the lawn, simply because he does not enjoy doing it? It is righteous for him to heave all the chores upon her so he can "relax" on Saturday? There is something to be said for treating others the way we want to be treated, and a man loving his wife the way Christ loves the church- sacrificially.
A believing husband who refuses to lead his wife and children even after prayerful requests from you and numerous appeals, needs to be given notice that you will be speaking to the leaders of your church about this. Your husband needs to be confronted biblically by the men in your church because this is a matter of biblical disobedience! And, I might add here that his response to this information will be shine a bright light on his heart!
This is the purpose of Matt. 18 which is intended to be for the purpose of restoring the sinning brother. Please, please do not look upon this precious passage of Scripture as "kicking him out of the church!" These verses are intended for restoration.
Sometimes, each of us needs a reminder that love is a verb, and love means sacrifice, and love means there are just times we do things we simply do not want to do for the sake of obeying God. We also need reminders that we are to not live for ourselves, when we are married there is another person to consider. Even an unbeliever gets that.
If your husband is not a believer, and has plain old refused to take any leadership role in the home, then you must accept that God has sovereignly allowed it to be this way in your marriage. You would then fall under the 1, 2 Peter category of suffering for righteousness sake. I would encourage you to do everything to commit these sweet books of the Bible to memory. You can continue to present him with leadership opportunities, but realize that his heart is darkened and he does not obey the same Lord as you do. Pray for him daily and be a good and loving wife to him in spite of, no, because of his unredeemed state. You may be the only representation of the Lord Jesus Christ he has ever known.
Love him like Jesus.