There are 2 parts to a step-parent adoption:
1. Termination of the parental rights
of the biological father. You must have specific grounds for the termination. I cannot tell you whether you have sufficient grounds because I don't know the specific facts. But, I can tell you that they must be very bad facts, like he abandoned the child and has had no contact. Another ground is that he has been ordered by a court to pay child support
and he has refused to do so for 6 months or more.
You will have to notify him of the proceeding. This is done by serving him with citation. He will then have a certain period of time to respond. If he does not respond, or if he ignores the citation, you will be able to terminate his rights by default.
If he does respond and contest the termination, you will have to prove the grounds that you are alleging to justify the termination of his parental rights.
I do not know if he is paying child support. If he is not and he contests the termination, the court will order him to pay child support. If he then goes 6 months without paying, you will have grounds for termination. In addition, once he realizes that he is going to have to pay child support, he may agree to the termination.
2. The second step in a step-parent adoption is the adoption proceeding itself. This cannot happen until the natural father's parental rights have been terminated. As part of the adoption process, the court will order a social worker to conduct a home study and make a recomendation as to whether the adoption will be granted. Your husband's DUI and house arrest will come to light at that point.
The point is that your husband's DUI is not an automatic disqualification for an adoption. It is one factor among many which the social worker, and then the judge, will consider in trying to decide if the adoption is in the best interest of your child.
I hope this answers your questions. If there is anything that you do not understand, please let me know and I will be to explain further.
In the meantime, please click "Accept" so that I may be paid for my answer and any subsequent follow ups with you.