Is this part of schizophrenia or something else?

My boyfriend is diagnosed with schizophrenia. Our relationship is not doing well, and his condition is getting worse rapidly (namely his delusions). One thing that I haven't been able to address properly with him is his lack of boundaries. He seems to have a good grasp on boundaries he's created for himself, but either doesn't see or care about the boundaries of others. Finds it ok to walk through people's yards, stops strangers to ask for things or interrupts them to say something not relevant. I love him very much, but when the habit started of him ignoring my requests for respect of my boundaries (addressing what they are of course) and then often degrading me in long lectures and irrational defenses and putdowns, I became very worn down and hurt. He doesn't seem to see the problem and as it got worse I began to question if this is even part of his schizophrenia. It occurs even while medicated but becomes worse when off his meds.
Either way, he also goes through cycles where he will sometimes display traits that strongly link to antisocial personality disorder. When he is like that, I barely recognize him and my emotions and psyche feel terrible around him. I could give and give and give and have nothing left for me, and he'll want more, but if I complain, discuss, say no etc. it leads to events that leave me completely defeated and confused. Walking away is what I feel I might need to do to protect myself regardless of who could be doing what, because it's become unmanagable. I don't want to leave him while he needs support and isn't doing well, but I'm deteriorating too in this situation.
I do feel if I could gain better insight into what I'm dealing with, I'll be able to make that decision with more confidence.
Is boundary crossing and combativeness a part of schizophrenia and if so how is it properly handled by loved ones? If it's not part of this disorder, what could it be and how does anyone else handle it (bar leaving of course).

I don't know what that's part of, but I've never heard of a Schizophrenic doing some of that stuff. It is possible he has Schizophrenia and a personality disorder, but hon, if he's wearing you down and screaming at you, insulting you, and all around putting you down, it's time to get out. What all is he saying to you?