Insurance Battles continue

Did I mention we sent in the official written claim to our insurance? We also faxed a copy of all the denials, and letters promising coverage previous to the birth, to the birth center's billers.
Jasper is six months old now, and they've still denied every claim, after promising coverage before his birth.

I'm totally at a loss.

We just received another denial of benefits in the mail today. This time, they've yet again chosen new reasons to deny. This time, they're also much more cryptic reasons - not so obvious that we should appeal:

"This procedure or supply is part of the global service. These charges are not eligilbe fore separate reimbursement."

and then follows:

"Your claim my have been separated for processing purposes. An additional charges will be processed as soon as possible."

In other words, we separated these items for billing purposes, and deny your claim because these can't be billed separately. At least that's what I'm understanding here.
It also shows the chart for out-of-network coverage... when they told us they would cover at in-network rates.

I can't believe this insanity!