I sent an email to NJTransit asking if I could use my monthly pass (NYP-Madison, 11 zones) to get to EWR as well. Their reply:

Dear Customer,

You may use your monthly pass to travel to the Airport Station. Once
you get
off at the airport station, you will need to pay the $5 access fee to
get past
the fare gate to the monorail.

We hope this information is helpful and thank you for your patronage.

Sincerely,

NJ TRANSIT Customer Service Department

I guess the access fee has gone up from the $5 they mention above to $7.