Biblically, the husband is the head of the house.
One mistake couples with blended families often make, and that includes many Christians, is not coming together as one family. Blended or not, when a man and woman marry they become one and their children become theirs.
In the best case, the husband and wife would come to agreement regarding any and all of the children. If a mutual agreement cannot be reached, then it falls to the head of the house to make the decision and for the wife to accept that.
The children need to know that they are accepted by both parents as their child, that they are loved, and that biological parent and step-parent will stand together in the raising of them.