You should speak with a local family lawyer about your options to involuntarily terminate the biological father's rights and have your husband adopt him. Different family courts in Texas treat these cases differently so it's important that you speak with a local attorney.
In all cases involving children, the court is obligated to do whatever it finds is in the best interest of the children. If you ask a court to terminate his parental rights, you need to be prepared to show that terminating his rights is in the best interest of your son. The fact that your husband is willing to adopt him would help your case. Cases such as this are very dependent on the surrounding facts, so I recommend you visit with an attorney experienced in this area and give him or her all the facts you can think of.
This is a general answer and does not constitute legal advice. By answering this question, I am not creating an attorney/client relationship, and no such relationship will be created unless a representation agreement is signed by both you and me.