Hi Hopefulgirl
I don't think jealousy is a BPD trait under DSM4 or DSM5. Neither is NPD. I keep away from diagnoses--I'm not a doctor. I would shy away from combining a general dislike for someone's behaviour with pathology. Problems with going into this are that it may create victim figures, skirt the main issues, and create harmful generalisations.
If it provides some comfort, you may think of the behaviour as indicative of a level of confidence in himself. This level of confidence may belong to either a very confident person, or indeed, a narcissist by OED's definition. Example sentences (OED online) include this one:
"They are cunningly manipulative narcissists devoid of consciences."
Whether this person is healthy or not is another matter.
