Someone already mentioned the DBT workbook, which I am seconding. Get the teacher’s manual as well if you can as it provide answers, examples, context and connections. DBT therapy is the gold standard for BPD.
Studying with him and learning DBT skills together can help so you have a common language and toolkit. In general, I would say DBT programs teach a lot of things, not just discrete skills but greater self-awareness overall. CBT can sometimes make BPD worse.
Secondly, something I wish I knew at the beginning of my treatment is that BPD is treatable and with the right support it can even go into remission. Personalities are malleable. If he learns new survival, emotion regulation, interpersonal and coping mechanisms to replace the maladaptive ones he uses now, he can effectively be rid of BPD altogether. I’ve heard it characterized as being like having diabetes, something to just manage once it gets under control.
Third, some small lifestyle changes (called ”PLEASE“ in DBT) you could do together or support him with can make a big difference!
As for emotional outbursts, I’ve found that when my boyfriend and I argue, if we orient our bodies toward each other and hold hands it’s hard for me to stay angry. Rather than my usual escalation, I am able to see him as my loved one and less “splitting” occurs.
Finally, you sound like such a loving, supportive partner. He is so fortunate to have you.