I finally managed to solve this problem on my own:
Jabref was encoding the bib-files in 16bit and Bibtex was expecting 8bit-code. After switching to 8bit in the Jabref-options the problem solved itself.
Thank you so much for all your efforts.
UPDATE
In WinEdt 9.1 build 20150713 the bug described below has been solved.
Simply use
\addbibresource{References/chap1.bib}
\addbibresource{References/chap2.bib}
\addbibresource{References/chap3.bib}
\addbibresource{References/chap4.bib}
and biber will compile your bibliographies correctly.
ORIGINAL ANSWER
The correct way is to use
\addbibresource{References/chap1.bib}
\addbibresource{References/chap2.bib}
\addbibresource{References/chap3.bib}
\addbibresource{References/chap4.bib}
But you are using WinEdt 9 and there is a bug in the compiler script for BibTeX and biber which prevents biber to run successfully when you redirect your auxiliary files to another folder.
To circumvent this (it will be fixed in the next release of WinEdt), open the file BibTeX.edt
(it should be somewhere like C:\Program Files\WinEdt 9\Exec\TeX
), then open the Options Interface and click on "Advanced Configuration".
Now click on the button "Create and Open Local Copy". A modifiable local copy of BibTeX.edt
gets opened.
Just after the line
IfIStr("%$('%!9-Executable');","bibtex.exe","<>",!"LetReg(3);");
insert the lines
IfIStr("%$('%!9-Executable');","biber.exe","=",>
!|IfStr('%O','%P','<>',!`LetReg(3,'--input-directory "%P"');`);|);
Now save the file and the job is done.
Try recompiling your file and now WinEdt correctly runs biber on your bibliographies.
Best Answer
\bibliography{../../bib}{}
is correct and works for me, after I correct an unrelated error. The .aux files needed to be cleared and I needed to ammend the bibliography style, then the above works. Thanks a lot guys for your help!