You mention elsewhere that your children are still young, so I suggest you not raise this with them until they bring it up (as they will eventually). By then, they may realize that some of their friends face the same situation, and this could help them accept it.
If they do raise the issue, you probably don't need to go into great detail, but simply explain that at present their father doesn't wish to participate in the activities of your church. More likely, however, they'll ask him instead of you (or at least in addition to you), and I hope you can encourage him in advance not to discourage them from going to church. If your children have become involved in the church's youth group, choir, or other activity, they'll be less likely to follow his example.
If they are active in some way, from time to time they may be participating in some special program -- a concert, Christmas program, ball game, etc. This would give you (and them) a reason to invite him to the church, and might help break down his resistance.
The real question, however, is this: Why is he opposed to attending church? Is it because he doesn't want anything to do with God? Whatever his reasons (or excuses), pray for him, that God will open his heart and mind to Christ. Pray for yourself, as well, that both your husband and your children will see Christ in you. The Bible says, "In everything set them an example" (Titus 2:7).