Did a doctor tell you he has brain damage from drug use? Again, you're assuming, unless a doctor has said that to you.

The DBT workbook does not mean a diagnosis.

What's dangerous about this way of thinking is it allows you to explain away his abusive behaviors by saying it's mental illness, and instead of putting down your foot about the unacceptable, you try to work with the behaviors because you have empathy and understanding, yet it's abuse which is being allowed without repercussions.

He should be in therapy, not just working with a workbook. He needs a real therapist. If that had happened to me, I would be insisting upon therapy and I would probably be insisting upon a formal separation in the home without affection, etc.

You say you get along great, but he threatened to call the police and accused you of abuse in front of your daughter. That is appalling behavior. Absolutely appalling. And so far, there's no repercussions.