Hi Thorsten,
If the response comes as a multipart message (rather than PDF embedded inside the JSON) you can have a look at this link from a few weeks ago:
https://community.appeon.com/index.php/qna/q-a/http-client-multipart-response-body
I wrote a test multipart parser which I attached in a reply to the above question. It has a an example of how to use it. Basically, it will will take a multipart message/response and split it into it's separate parts including headers and body for each part. If that suits your use case you could use that parser to split the response into the JSON and the PDF parts. The headers for the PDF part should tell you whether it's binary or base64 encoded so you know how to deal with it.
The specific case in the above question was regarding XML and the response from a SOAP call, but the multipart format is pretty universal so it should be applicable to your case. When I wrote the parser I tested it with multipart mail messages.