They have children under 18, so splitting up is unappealing since broken homes are both unpleasant for children and major predictive markers on dysfunctional adulthood.
For this reason, I believe the couple should stay together. It is my opinion that non-Christian couples who marry aren't truly married anyway. They haven't made their vows under the authority of the Creator God. As Christ-followers we should not be advocating further family dysfunction by demanding that they break up.
One half of the unmarried couple becomes a Christian while the other half cannot take Christ seriously (at least not yet).
We have to be really careful here. It drives me absolutely insane when a pastor starts droning on about how the men in America are not living up to God's expectations. They chastise us, berate us, and ultimately tear us down until we become very small in the eyes of our wives. It is as if Satan's feminist sledgehammer has finally penetrated their skulls so there is no more thought process left. It ultimately leads to great women of God succumbing to the pressure of leaving their husbands for "better men of God."
That is exactly what happened to me. I lost my wife, my son and my business, all because she thought it would be better to run off with a "better Christian man." It has been by far the most brutal attack Satan has ever leveled against me.
What is the right thing to do here? Is it really - as I myself suspect - the duty of the Christian to leave their partner? Some Christians marry non-believers but as I understand it, this too is advised against, with what appears to be good Biblical evidence to support it.
I don't want to call you out here, but this is my point exactly. When you say "the duty of the Christian [is] to leave their partner," it just plays into Satan's hands. I know that by not being married, this couple is living in sin. I get that. But please think about the children they have together. Are we going to advocate breaking up a home just so we can say they "did the right thing?" By keeping this couple together, married or not, they have a much better chance to serve God.
I would give anything to have my family back.