This is a hard question to answer, and I appreciate the anquish with which you must ask it.
If you were married in a Catholic ceremony, you would promise to do all within your power to have your children baptized and raised as Catholics. Your non-Catholic husband would not be required to make any promise, but would need to be informed that you had made such a promise. So the primary responsibility for raising your childen as Catholics would rest with you.
In your present situation, I would encourage your desire to have any children of your marriage baptized and raised as Catholics, but you will have to be prepared to do it on your own. You mention that your husband has stated that he does not want take part in the childen’s spiritual upbringing. This is unlikely to change. He has made clear what he will and won’t do. He will allow you to raise the children as Catholics but he will not participate in their religious education. You can’t force him to do something he doesn’t wish to do. In choosing to raise your children as Catholic, however, you will find support from your local parish and the religious education programs it offers.
I believe you owe it to yourself and to your husband to explain to him clearly why it is important for you to be married in the Catholic church, for it sounds like it truly is. A single honest and complete discussion about this could serve to clear the air. Again, insisting that he do something he’s not willing to do will only breed resentment. But he needs to know your true feelings about this. You will need to decide whether you wish to stay in the marriage if your spouse is unwilling to support you in an area that means so much to you. If the answer you give to yourself is “yes”, than it won’t be helpful to continually bring up the subject again, but you can pray quietly for your husband each day. You can also ask God in prayer to bless your marriage and continue to support you in your own faith.