Contact Michael Question 13. About those who have lived together and one of them accepts the Lord, while other partner is on way to acceptance but still doubtful. 2 While they behold your chaste conversation coupled with fear. But let it be the hidden man of the heart, in that which is not corruptible, even the ornament of a meek and quiet spirit, which is in the sight of God of great price. Christ condemned divorce in Matthew 19.
Separation is often a precursor to divorce.
Separation does not often strengthen the bond between husband and wife, but weakens it. If they stay together, perhaps the reluctant one can be persuaded by the example of the Christian to investigate further and become a Christian also. Then YES they should separate. They should separate to stop comitting fornication. To obey the gospel of Christ, and to continue to commit fornication, indicates no repentance.