You cannot apply based on US permanent residence. You must use the process based on citizenship at the time of desired entry.
Finland and Germany are lumped into this because they also refuse to accept Filipino paperwork, according to the Apostille site. This is despite their agreement to the convention, of which Philippines is a part.
Schengen visa rules dictate that you must apply at either the country you enter first or the country you are planning to spend the most time in. In our case, Greece was the answer to both of those questions. Had we applied to Italy, they would have refused to process the Schengen visa and told us to apply at Greece, who refuses to accept the papers.
We asked the Tampa consulate if it was possible to apply in Atlanta instead, and they agreed to this request. We did not show up to the Atlanta consulate blind or without their permission.
The reason I brought this into the discussion is because an EU country is very difficult for us to move into until my wife and daughter become US citizens. I expounded on the experience because I was asked.