You need to see a family lawyer on your own, but you two should see one together as well.

How this goes is entirely based on how amenable this woman is to working with him, and frankly there are limits to what courts will allow even when she's willing to work with him. Courts are really protective of kids, especially tiny babies, so your husband likely won't be able to get a single overnight until the kid is over 6 months and may not have a chance at joint custody for YEARS.

Which means that your husband is going to have to prioritize keeping the peace with this woman.

If he pisses her off (like, you know, by dumping her while pregnant) or she just decides to be vindictive and refuse to give an inch, here is what you're looking at in America at least. (frankly most other countries I know of are even less kind to unwed fathers)

• He is legally a stranger to both her and this child until paternity is established. She does not have to tell him she has had her baby. She could disappear and hide she had the baby. Even if she tells him as soon as the baby's born, he'll have to file for paternity and will have zero rights to even see the child until he's on the birth certificate.
• It takes time to go through establishing paternity. I've seen it take on average 6 weeks, but that's from the time he files. So if he doesn't find out the baby's born for a month, then the baby could be 10 weeks before paternity is established. In that time, the mother has established herself as the primary caregiver and residence.
• Your husband will have no relationship with this child, and small babies are very vulnerable, so he will likely be started with brief supervised visitation. At most a few hours a week, maybe less. He will have to go through court to gradually increases this with time. He will have to be on his best behavior the entire time (even if she's a jerk)- missing a day, being late, or doing something she doesn't approve of could be cause to have his time decreased (she'd have to take it to court- but she can)
• That means he'll be starting out by paying the highest amount of child support the court can order. (again why you want to protect your kids first)
• Even when he gets unsupervised visitation, there'll be restrictions on it. He'll have limits in where he's allowed to go and what activities he's allowed to do and who is allowed to see the baby. She'll have to push for these in court, but if she gets the judge to say the baby isn't allowed around you or his parents or your children- he has to honor that. If he violates a court order, it'll really hurt his visitation and custody case.
• Jurisdictions usually consider tiny babies too young for overnights until around 6-9 months, sometimes even longer. So he won't even get a single overnight with his child for many months. As you can imagine, that means the child will be fully raised according to her parenting method and schedule- which your husband will have to maintain for the child's well-being.
• Even once he's established one overnight (which may be once a week or EOW), it takes many months even years to work from one overnight to joint custody.
• Courts work by precedent- they want to keep the child's life as stable as possible. Every single time he goes to increase his time with the child, he has to convince him that it's a better option than keeping the status quo. Some jurisdictions are more amenable to this than others.
• Even once he gets joint custody, that isn't equal and full rights as if he were a sole parent. He likely won't be able to take the child out of the state without her permission. He may have to get her permission for things like medical treatments and summer camps and after school classes. You will have zero say in this- he must agree with how to raise this child with her. She can put in a 'right of first refusal'. Which means that if he himself is not available to care for the child, he MUST give her the choice of taking the child- meaning that you won't be able to just care for the child when he's not available. If he is unavailable too often, he can lose joint custody.
• All of this is reliant on everyone being civil and him having a good lawyer- if this gets really contentious and ugly, then it can drag out even longer.