Very hard to get straight answers....does an NJT monthly from Murray Hill to HOB or NYP entitle the holder to unrestricted travel on HBLR (HOB to Jersey City, for instance)? NJT conductor I asked said he would try to find out but apparently there's a history of flip flops on both Newark Light Rail & HBLR. He hasn't come back to me on it and web searches so far haven't helped.
As a random GUESS and nothing more, I believe it is likely that the monthly pass is not valid on HBLR as that line is operated and maintained by 21st Century Rail Corp. (part of the DBOM contract entered when the line was being built) and is only branded as NJT. I would imagine they'd want to keep thier fare system to themselves.
I'm probably wrong, though. Sorry I don't have a definitive answer.