There is no requirement for tithing in the Catholic Church.
I’ve been married happily for 40 years to my husband. My advice to you is to submit to your husband in this matter.
Discuss a reasonable amount that he is happy to give, and leave it at that and do NOT dwell on it or keep worrying about it. God honors your submission to your husband.
There is a reason your husband feels uncomfortable with giving a tithe. If he does the family finances, it would be good to make sure you know what is happening with his paycheck and just how “tight” the budget is. It’s possible that you and he are on the edge of poverty and he knows it, and he is trying to make sure that you are happy and that you both have enough cash to pay your bills. Sometimes there are debts that one of the spouses doesn’t know about.
The important thing is that you trust him and demonstrate your trust and confidence in him. I’m not talking about being a naive little airhead who ignores signs that your husband is in trouble (gambling, porn, etc.). If you have a feeling that something like this is going on, definitely look into it.
But if he seems to be working hard and giving you enough money to pay for your responsibilities in the home, then don’t worry about tithing at this time in your marriage.
Keep in mind that many people in your parish are comfortable financially and able to give above and beyond a tithe. Your family will hopefully get there someday, but in the meantime, let these others make up for your smaller amount of donations.
Also keep in mind that even if you have a paying job, too, along with caring for your home and family, your husband may still feel uncomfortable with a tithe of this paycheck. So getting a job is not the answer.
One thing you can do if your husband is willing is establish a “blessing jar” in your home. When something good happens in your family, contribute a coin–it can be a quarter, a dime, even a penny, if that’s what you feel comfortable with–whatever. Once a month, give it o your parish.
Another thing you can do is give up a “treat” that you always buy for yourself at the grocery store, or any store. E.g., if you treat yourself to a Starbucks once or twice a week, give it up and donate the money to your parish instead. If you have children, don’t ask them to give anything up–it’s more important that children see the generosity and love of God. Make sure they give their dime or whatever to the offering and make sure they realize what the money is used for.
Finally, consider a “tithe” of time. Your parish will love you! I know that often young wives are very busy and don’t have a lot of time, but if you can carve out even an hour or so a week, volunteer for something at your parish. We have a crew of people in our parish who volunteer to help dust once a week–they have a good time doing it, and it helps cut the cost of hired cleaning services (so in a way, you ARE tithing “cash!”). Ask your parish where help is needed and than volunteer that valuable time.