There is a verse in the New Testament of the Bible that might give the impression that the faith of a spouse can impart salvation to others in their family.  Here's what is written: "For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband."¹

Under Judaism, if a Jewish man had married a foreign wife, they were commanded to send them away, even the children if they had children by them.²

In (1 Corinthians 7:12-14), the apostle Paul is telling those who are Christian that this does not apply under Christianity.  Christians who have a non-Christian spouse are not to send them away (divorce them.)  The Old Testament commandment to send them away no longer applies to the people of God under grace.  Both the children and the non-Christian spouse are sanctified (set apart) by the Christian parent and are not to be considered unclean and sent away.  They are considered holy (set apart) in a positional sense.  That's not to say, however, that they do not have to come to a saving faith in Christ Jesus as Lord and Savior as to their salvation.  No one can save another through their faith.

Bible References:

¹ (1 Corinthians 7:14)

² (Ezra 9-10; Nehemiah 13:23-25)