I am married and I have had a baby by another man, but my husband has agreed to take the child on as his own, am I breaking the law by registering the child in my husbands name and not the fathers name.

It would help to know what State you are in first. But in general most states recognise the husband of a marriage to be the father of the child regardless of DNA. That being said the laws vary widely as to if it can be challenged in court or have time limits to such an action.

If you were married at the time you gave birth, many US states view the husband as the father, ( even if he is not) unless he challenges it.

Has the real bio father been notified and is he OK with this ?