What should I do if I want to tithe, but my unbelieving husband doesn't?
I think the simplest thing is to say that if you originate no income, then God doesn't expect you to give any income. So, that's a simple answer. You could stop right there.
But that's not going to satisfy you, probably, and you want to hear more than that.
I think the way a husband like this would work is that she could say to him, "Could I count any of your income as mine and have discretion over it? Because I work: I keep this house, I keep our children. I'm full-time here. This is a partnership. I know that you go outside for work, but I do the home. I make this happen."
And then, not to deceive him in any way, but totally open and above board so that he knows where she's going, she could ask, "Can I count some of your income as discretionary for me? I know that it's not your preference to give money to what you don't believe in, but you know that I believe in this, and it's helping me—I hope—be a really good wife for you. I'm faithful to you. I serve you. I'm physically and sexually there for you. I admire many things about you. I'm glad I'm married to you." (I think a Christian wife can say those kinds of things to an unbelieving husband.)
And then meekly say, "I know you don't want us to give ten percent of our income away, but can we just come up with a number that is mine to work with?" And I would guess that an unbelieving husband would do that. At least, that would be the direction that I would go. Then she would tithe what she senses and he agrees is her appropriate share.
It's sad when you have to think like that. In my marriage, I like to think that all of my money is Noel's and all of her money is mine. If she gets some royalties because she does a children's book, and puts it in the bank, I'd like to think, "That's our money. We can give that to the church. We can do with it whatever we want." And everything I get from the church, I want to say, "It's there!" I don't like separate bank accounts. I just think we ought to be totally at each others' disposal and have our money be each others'.
But that's not going to work where a husband doesn't have your same values and isn't following Christ.
So that would be my approach for the wife: seek her husband's willingness to count some of the money as hers, and then ask if she can do with it according to her own priorities.