CHR is not, technically, a constitutional commission because the 1987 Constitution listed down only three such commissions under Article IX: CSC, Comelec, and CoA.
"Section 1. The Constitutional Commissions, which shall be independent, are the Civil Service Commission, the Commission on Elections, and the Commission on Audit."
But the CHR was also created by the 1987 Constitution through Article XIII, Section 17:
"Section 17. (1) There is hereby created an independent office called the Commission on Human Rights."
Interestingly enough, I came across a news article in 2014 which reports the dismissal of CHR Commissioner Coco Quisumbing "for violation of Section 7 (d) of Republic Act (RA) 6713, and grave misconduct for requesting and/or receiving the salary differential" of a former employee. Does this mean that the CHR commissioners and chair are NOT impeachable officials? The Ombudsman ---Aling Conching--- dismissed a commissioner in 2014.
And since the CHR was constituted by an EO (163) and not a law passed by Congress, the president can pretty much rewrite the constitution of the CHR by writing another EO supplanting EO 163, as long as it does not conflict with Article XIII.
Am I right? Not a lawyer, sorry...