Then come mysterious words. It cannot possibly mean that the unbeliever is sanctified in the sense of being saved, or literally made holy, because that can only be done by repentance and faith, by believing in Christ and conversion and grace; so it cannot mean that, because that would introduce a massive contradiction in the Scripture.
Another way of viewing this passage is to see the sanctifying effect not as something that changes the unbeliever in any way, but which simply prevents the unbeliever from having a harmful effect on the believer. Calvin says, ‘Paul therefore declares here, that marriage is, nevertheless, sacred and pure, and that we must not be apprehensive of contagion, as if the [unbelieving] wife would contaminate the [believing] husband.’ He adds, ‘It might seem as if a believing wife contracted infection from an unbelieving husband, so as to make the connection unlawful; but it is otherwise, for the piety of the one has more effect in sanctifying marriage that the impiety of the other in polluting it.’ The apostle proves that the believing wife has this effect on her unbelieving husband, or vice versa, by a consideration of the state of the children. What does he have in mind? Is he still thinking, when he says this, of the children of a mixed marriage (believer and unbeliever), or is he thinking of the more general case of the children of any marriage involving a Christian? If the former, then the argument could be this: Given that the unbelieving husband pollutes the believing wife, then he also pollutes the whole marriage including the children. But since the children are holy, he evidently does not have that effect on the children, and therefore the wife is also unaffected by his unbelief. But if Paul has in mind the children of two believers, then the argument might be this: Since the children of believers may well still be unconverted, then without the sanctifying effect of the believing parent on the unbelieving child, the child too would be unclean. However, such children should not be regarded in this way, for they are to be seen as holy within a believing family. This does not mean that they are now sanctified in the sight of God any more than the unbelieving husband is. Without personal faith that is not possible. But to the believing member of the family they are to regarded as holy and can transmit no pollution. This is not about any improvement in the unbelieving spouse or in the children; it is about the protection of the believer from the effect of being in such a close relationship with an unbeliever. That Christians can have children is obvious from the command to go forth and multiply. But if unbelieving children (who might not come to faith till later in life) pass a contagion to their believing parents, then in commanding them to have children, God would be telling them to do something that harmed them. That is impossible. The language suggests that Paul has in mind this more general second case. If so, the very interesting assumption behind his reasoning is that the children, like the unbelieving spouse, may not be converted, and yet they are your children and you live with them in a close family unit without incurring any pollution from them. This assumption refutes any use of this verse to prove that children of believers are also in the covenant. If that were so, regardless of their person faith, then the unbelieving husband would also be in the covenant because of the believing wife, which is evidently false. The assumption of the verse seems to be the opposite: that the children are not in the covenant but are in a state of unbelief until they are converted, and yet, for all that, they do their believing parents no harm.