We have a 3.5-year-old daughter. Since she was born, his outbursts have become increasingly frequent and increasingly violent (consistent, as my attention was necessarily diverted to taking care of the baby).
Well it looks like your therapy training has given you some insight into your own situation. The way I see things, your husband is getting worse because you have a young child, and as you wrote, your attention has been necessarily diverted towards the baby. You see, pwBPD are triggered by feelings of abandonment and can get upset whenever 100% of your attention isn't on them, even if the reason is you're busy with his own baby! I suspect there's a little regression going on too. He sees the baby gets your attention when she fusses and cries, and he does the exact same thing.
On these boards I've seen references to pwBPD lacking "object constancy," the ability to maintain a stable, positive emotional connection with a person even when they are absent or when they feel angry/frustrated with them, understanding they are a whole person with both good and bad qualities. For pwBPD, object constancy seems to be a challenge, as their black-and-white thinking dominates. So if you leave, or you're busy with something, or you're tending to your precious daughter, your husband assumes the worst. He might think, you don't love him and don't pay enough attention to him anymore. In short, you are not meeting his needs! And by the way, it's all YOUR FAULT for making him feel this way. I think that's what your husband means when he's hitting himself. YOU are the one who unleashed these negative emotions inside him. He has been displaced and upstaged by his own kid. It's sad, but it sounds like inside he has the emotional maturity of about a toddler. At the end of the day, he is extremely insecure, and he has unending emotional needs for your constant attention and reassurance.
In my opinion, if your husband is actually violent--bruising himself, threatening to use a knife--I think you need to call 911. You used the word "violent," and that's why I'm writing this. You have a young daughter to think about, it's a very small escalation to turn his aggressions onto her and you. In my opinion, you need to have a firm boundary when it comes to violence, and call 911 straight away. One would hope that one single call to 911 would teach your husband that violence isn't allowed in your home, and violence would be off the table. If he doesn't learn, I think you have to seriously consider the safety of your daughter.
As for shouting and obscenities in the home, while it's certainly not ideal, it does happen, even in families without any mental illness. In my opinion the rule for me would be, no shouting or obscenities in front of the children. If he started a scene, I'd remind him of the rule, try to steer him outside or out of earshot, or possibly leave the scene with the child under my wing, maybe go for a walk, a drive, a trip to the library. With some luck he'd have time to calm down during this "adult time out."