Waiving parental rights in Oregon? My husband might have a child on the way and wants to waive rights.....

He had a one night fling with a woman who said she was on birth control... surprise she wasn't! What a wake up call for him. He told her he did not want the child. That she should adopt the child to give it a better life. She has decided to keep it and raise the child on her own. He is obviously torn on what he should do and what morally the right thing is to do.
He does not feel that the child being in both homes as joint custody will be best suited for this child. What is Oregon law for waiving rights?
On the hinder for my question, what are Oregon rights for a father to get full custody? She is very trashy and i have proof she was a prostitute. Not the kind of mom that should be raising a kid. He hasn't taken a paternity test yet and the child will be born soon. Thanks in advance.