Their bio father only wants to be in their lives when its convenient to him. He has never helped financially with them and has even laughed at me if I were to ask. My husband now, has been there for them and they love him. What can I do about him adopting?

1. Get a lawyer. I am astounded at the number of people that would go into an adoption situation with no lawyer. While you CAN do it without a lawyer, you can also set a bone without a doctor. I don't recommend either.
2. Ask the biological father if he will relinquish rights. If he will, then this should be easy-peasy. If he's not involved, he may be willing to sign over rights to get out of future child support.
3. Go to court and have the adoption finalized.

If the other biological parent is willing, step-parent adoptions are fairy easy and generally pretty reasonable in price.

PS--if you never got a support order, he has no legal obligation to pay child support. You may want to go after him for support first so that he has incentive to relinquish his rights.

If their father doesn't want anything to do with them it should be a fairly easy process. You first decide what adoption lawyer you want to go through. (I will never ever ever recommend trying an adoption without one) He/She will get the court date and prepare all the paperwork. You can simply ask the father to relinquish his right to let the adoption go through. If he doesn't agree at first you still go to court and try your case in front of the judge.

You said he doesn't pay support. Do you have a court order for support? That makes him legally responsible to pay. If you do have on you can go to court to have it enforced.