Perhaps the only passage in Genesis that explicitly states a man’s role in relation to his family is Genesis 18:19. God says of Abraham,
For I have chosen him, that he may command his children and his household after him to keep the way of the LORD by doing righteousness and justice, so that the LORD may bring to Abraham what He has promised him.
The New Testament sees in the relationship between Abraham and Sarah an example which should be followed today.
Likewise, wives, be subject to your own husbands, so that even if some do not obey the word, they may be won without a word by the conduct of their wives, when they see your respectful and pure conduct. Do not let your adorning be external—he braiding of hair and the putting on of gold jewelry, or the clothing you wear—but let your adorning be the hidden person of the heart with the imperishable beauty of a gentle and quiet spirit, which in God’s sight is very precious. For this is how the holy women who hoped in God used to adorn themselves, by submitting to their own husbands, as Sarah obeyed Abraham, calling him lord. And you are her children, if you do good and do not fear anything that is frightening. Likewise, husbands, live with your wives in an understanding way, showing honor to the woman as the weaker vessel, since they are heirs with you of the grace of life, so that your prayers may not be hindered (1 Peter 3:1-7).