First would definitely rule out medical issues.
Second, how much exercise is he getting?
Third, how much, if any, training has he had before baby?
It sounds like he was maybe over-stimulated (playing ball, etc), got on the couch, maybe didn't expect the baby to be there, and bit. Definitely could be jealously, or resource guarding, or over-stimulation, etc.
If you can, I would begin associating everything with the baby as positive. Baby cries = Tibbs gets a treat. You pick up baby = treat. Take baby for a walk in the stroller and have Tibbs walk beside. Everything that baby does needs to = good things in Tibb's mind.
I know how easy it is with a new baby to put the dog aside for a bit, it happens... but sometimes people don't realize just how much the dog is being "ignored" (compared to what he was used to) and how big of a change it is for a dog. It takes a lot of adjustment. You are right - your dog should not be biting your baby. I do agree that I would implement the NILF program.
I do believe exercise could be a big help in this in general, so I am curious how much he gets. Like TRUE exercise -- not just running around the house, etc. Give him a job to do - maybe even get him a little doggy backpack to wear with something very light on your walks - give him a job to do, to feel needed/wanted. Teach him to fetch you a diaper for the baby so he feels like he is helping.
Check out some of these sites, too:
Dogs and Babies…Learning to Live Happily Ever After
And a good article:
Mamas, Don’t Let Your Babies Get “Magnetized” to Dogs Dogs and Babies…Learning to Live Happily Ever After