Yes MSIE11 supports TLS V1.2, 1.1 and 1.0.
Use WinHTTP or WireShark to inspect the communication via browser and webserver.
You should be able to tell if your proxy / firewall is hindering communication, or if the browser is using (handshake negotiation) to request a (different encryption channel).
Without more information I can't troubleshoot your specific problems... A lot improved in (Win 8.1).
Edit: I think the problem you are having is with GCM being prioritized first in your cipher suite. GCM is not enabled by default (6) on Windows 8.1, IE11 will handshake negotiate down to the first cipher it supports, in your case DHE-RSA-AES256-SHA256.
(6) ttp://msdn.microsoft.com/en-us/library/windows/desktop/aa374757(v=vs.85).aspxhttp://msdn.microsoft.com/en-us/library/windows/desktop/aa374757(v=vs.85).aspx