This is a very important subject and we appreciate you inquiring about what the Bible teaches. The word authority is a very harsh word. It suggests that someone is superior to the other and unless we use the responsibility of authority wisely and kindly, we will do more damage than good.
Ephesians 5, beginning with verse 22, presents the husband and wife relationship. The Bible teaches that the man is the head and the wife is to submit. However, in this order of things, the Apostle Paul is not reaching that the wife or female is inferior in mentality to the husband or the male. He further emphasizes that the husband consider his wife as a part of his own body. This suggests a two-way cooperative effort with both parties benefiting.
When the inspired writers spoke of the qualifications of elders and deacons, they pointed out that the men were to have ruled their own houses well. I Timothy 3:3-5 (READ THIS NOW). So the Bible teaches that the husband has the ultimate authority in the home. How he exercises this is the mark of a great man - a great father and husband. He should never view his position of responsibility of one of master and slave, or dictator and subject. Rather, the Book teaches that he views his wife as a part of his body, Certainly the good father views his children as a part of himself. So, fathers, in your position as head of the family, into whose hands the authority has been placed, consider those members of your family as partners.
Let me emphasize the word partnership - a part of each other. Can you think of any decision that should be made that affects the whole family, that the father/husband should make right by themselves, without considering their wife or their children? If it concerns your job, should you not .talk with your wife and consider her feelings in the matter? It does affect her. A Christian father will take the feelings of the entire family into consideration. The Christian father does not exercise his authority in the family by simply saying, "I am going to do it regardless of what the other members of the family want or like, because I am the head of the house". This exhibits a lack of kindness, tender hearted and genuine love for your family.
Too often we feel that authority means that we make all the decisions. But it also means that we have the responsibility for the leadership of the family. The Christian father will, assume a predominant role in the religious training of his children. This will include not only Bible Study and devotionals at home, but examples in worship services. Your position of authority means that you are the provider - and this includes providing for their spiritual well-being as well as their physical needs.
The Apostle Paul tempers your position of authority by saying in Colossians 3:19, "Husbands love your wives, and be not bitter against them". This is meaning that you are to love them and not be hateful toward them, overly harsh, or inconsiderate. The fathers relationship with the children is also presented in Ephesians 6:4: "Children obey your parents in the Lord. …fathers, provoke not your children to wrath (or anger) but bring them up in the nurture and admonition of the Lord".- Be kind to your children and considerate. Then he gives the fathers specific commands to bring them up in the nurture and admonition of the Lord., This simply means that as fathers you have the RESPONSIBILITY to see that your children are taught the words of the Lord and learn the true meaning of Christianity. What better way can you do this than by the proper use of your position of authority in the family, teaching them correctly and also setting the right example.
The responsibility of authority that God gives to the father should lead the dedicated Christian father to gently and kindly direct his family in the paths that will best benefit every member of the family. He will oversee, not only the physical provisions of the family, such as food, clothing and housing, but also will see that their needs for spiritual teaching and guidance are met. Some fathers have tried to divide the responsibility of leadership into categories. Sometimes they will say to their wives, you be responsible for the house and children and I will make the living. While this may sound good, it is NOT a Biblical principle. The father has the position of authority and responsibility in the entire family siutation. Yours is a Big Job. Your responsibility matching your authority goes on after you have finished your days activities as you lovingly guide your family in the right ways of the Lord.