I’m not in the same situation, since my spouse was never Catholic. However, this is what has worked in our daily lives:
My spouse is very supportive of our family’s faith, but doesn’t believe in God. To support the children and I in our faith, he does not draw attention to his lack of faith. He attends Mass with me, stands and sits, and gets a blessing from the priest (like our children do) when I receive Communion. He is involved with our friends from church, and feels comfortable in our church community (although this took a while).
However, to stay honest to himself, he doesn’t say prayers (except on rare occasions, and then he is very careful about the wording, that it doesn’t imply a faith he doesn’t have). He will remind the children and I to say grace at meals, but will just sit quietly while I lead. He brings our family to a Rosary group to pray with friends sometimes, but then reads a book or watches the young children who wander off to play instead of praying with us. Your spouse can be honest while encouraging the children to pursue their faith, if s/he is willing. Be aware that our children are only 3 years old; this might play out differently with older children, and I would guess you may at least want to discuss your explanation if they ask.
For my part, I pray for my husband to be given faith. Fortunately, he appreciates this for what it is, and encourages me to persevere in prayer for him.
I absolutely encourage you to continue in your marriage, and keep seeking to bring your spouse to Heaven. If you haven’t already, check out the “St. Monica” thread on this forum (sticky thread), which is people praying for the conversions of their families.