The Old Testament basis:
Numbers 30 says that if a man takes a vow before the Lord, he is responsible to fulfill the vow, pure and simple (Num. 30:2). However, if a woman “in her father’s house in her youth” makes a vow, her vow is subject to her father’s confirmation or nullification (Num. 30:3-5). Now one striking thing to note is that this passage does not single out young men still residing in their father’s house. It only references the young women...
The New Testament basis:
...we see the same principles showing up elsewhere in Scripture, namely the New Testament: the husband is to take responsibility for his wife (Eph. 5:25-29). Paul says that the husband is to imitate Christ who loved the Church and gave Himself for her. Jesus took all our liabilities on Himself. He pays the debts that we owe, and He cancels the debts we should have never promised to pay with His perfect wisdom and justice [...] The husband is to view his wife as occupying the same position as his own body. This means that her troubles are his troubles, her actions are his actions, her vows are his vows.
In other words, if the wife decides to shoplift she is guilty of sins and crimes personally, but the moment her husband finds out about it, he incurs responsibility to act to put things right. In fact, he is arguably already responsible for the act before he knows about it because he is covenantally united to his wife. When she acts, he is acting. But he has a duty to respond, to lead her out of this situation the moment he hears of it. But the same principle applies to less lurid scenarios: a man is responsible before God to lead his wife. He leads by initiating discussion, planning, directing, and affirming some decisions of his wife and children and vetoing others.
For more, check out this helpful + biblical post