I had twins by a man who was not my husband and my husband will not sign denial of paternity what happens

If he won't sign denial, then he is accepting paternity.

First This has been moved from the Children forum since it's a question of law. Please exercise more care in the future where you post.

Second, ANY question about law needs to include your general local as laws vary by area.

In most US states when children are born to a married couple the husband is presumed to be the father. Unless a challenge is issued to this paternity the husband takes on the rights and responsibility as the legal parent. Who can mount such a challenge and what time frame they have to mount one depends on your area.