The Chief Ombudsman received five complaints about these decisions, and investigated them together.
In his final opinion released this morning, Boshier agreed with the NZDF that releasing some of the information would affect other nations' willingness to share it in future.
He also said much of the withheld information contained sensitive details which, if released, could prejudice New Zealand's defence and security.
However, in relation to government knowledge about the operation, he did not accept there was a basis for withholding the briefing material in full. He recommended release of four briefing documents and appendices, with some redactions.
"NZDF has agreed to this. I expect a prompt release," he said.
On civilian and insurgent casualties, Boshier also recommended the NZDF release the information it holds concerning the identities of insurgents killed during Operation Burnham.
During the investigation and after discussions with the Ombudsman's office, NZDF released some information on its website, including information about the location of Operation Burnham.
However, Boshier said the NZDF could have been "considerably more responsive" in how it handled these requests.
"NZDF didn't tell requesters or my office at the time [the information was released], and the information wasn't put on a prominent part of the [web] site.
"It has given the appearance of reluctance on the part of NZDF and requesters have understandably developed some mistrust as a result."