I am married to an agnostic who leans atheist, so you know where I’m coming from.
I think the questions that you would need to consider are:
- Is he an evangelistic atheist (tries to convert others to atheism) or agnostic atheist (I don’t believe in God, but I could be wrong and I can see how someone might reach a different conclusion), or something in between? I think a devout or evangelistic atheist would be very difficult to have a relationship with, but an agnostic atheist could be workable.
- How actively supportive of your faith does he feel comfortable being, and is he willing to be? How do you feel about that? This includes whether or not he will attend Mass with you, pray with you at any level, make time for you to attend Confession, practice no birth control but NFP and not pressure you about it, support you in Lenten fasts, celebrate Christian holidays, and generally how he will or will not value your faith. If he is evangelistic atheist, you could be in for a lifetime of conflict.
- How do you feel about living your Catholic faith if this person’s faith never grows? Can you persevere in praying for his conversion throughout your entire marriage, with God’s help, even if you never see the answer? Does he help or hinder your faith?
- And the most important question to answer: Is God calling you to this marriage? Pray, pray, pray, and note how your heart moves on this matter when you pray about it.
I find that being married to an agnostic is like facing in two different directions while trying to travel together - I am oriented towards God, while my husband is looking somewhere else. However, I believe that a greater chance of arriving at the destination together is worth a more difficult journey than traveling on my own and knowing that the man I love is that much less likely to find the right direction. At the same time, I find my desire to keep going is increased, since a loved one (my DH) may depend on me to show the way. I want to become a saint because I want God to have my husband’s heart, and I believe opening my own heart to God’s grace and converting myself is the best way I have to strengthen the connection between DH and God, since DH sees Christ mainly through me.
My husband is highly supportive of my faith. He attends Mass every Sunday, and reminds our children and I to say grace before meals (since he doesn’t believe that God hears prayers, he feels dishonest joining us in praying). When I am down or struggling, my husband reminds me to pray. It can work, and it can be quite beautiful - but it has to be the right two people, and it has to be God’s Will. Pray!!! That is the only way you can know for sure - I truly believe marrying a non-Christian is a rare calling, but one that God sometimes gives. If you are called to it, you will receive the graces you need to endure it in joy.
I say “endure”, because you will miss out on some of the joys of a fully Christian marriage - like praying with your spouse, or openly treating your sex life like a symbol of Christ’s love for his church. From what my priest said when DH and I married, you will also miss out on receiving some special graces, although your marriage will receive them should your husband ever convert and open his heart and your marriage to them. This makes sense to me - after all, unless your husband is also a Christian, you and him are not “two or three gathered in [God’s] name”, but if you together become two gathered in God’s name, “there [is God] in your midst”.
So . . . be aware that it won’t be a perfect marriage, and there are riches in Christian marriage that you will miss out on. But if God is calling you, and you truly love this man, it may be worth it. Just be sure before you get married. Oh, and make sure he understands that Catholics don’t do divorce

You want him to be fully aware of the nature of the vows so the marriage actually happens and you don’t need to seek verification of a null marriage later. You’ll need a dispensation to get married at all (an important technicality), and if he hasn’t been baptised then it will be for disparity of cult and that’s more serious than mere disparity of worship.
HTH,
-LFL