To summarize: no, you cannot. This is the exact point of DHE. In pompous terms, DHE provides perfect forward secrecy, which means that knowledge of the permanent server's private key (the one corresponding to the public key in the server's certificate) is not sufficient to decrypt past sessions.
Technically, when DHE is used, the server's certificate and private key are used only for a signature: the server signs its transient, newly generated DH public key; the client verifies that signature. So the private key is used; only not for encryption purposes. By having a copy of the server's private key, you could forge a fake signature, meaning that you could impersonate the server; but signatures do not hide data, so a passive-only attack (as you are proposing to do) cannot learn anything that way.
If the server uses DHE and you need to see the data, then you must mount an active attack, usually known as a Man-in-the-Middle attack. You pose as a fake server; you use your knowledge of the server's private key to impersonate the server; when a client connects, you also connect as a client to the true server, and relay data in both direction. The MitM decrypts data received from the client and reencrypts it into the SSL connection opened with the true server, and does the same in the server-to-client direction. That way, the MitM gets to see all the data, but he must actively work at the moment of the connection. He cannot do that after the fact, i.e. decrypt a past session that he recorded passively. Hence PFS.