This question is a little vague, and sounds more like a networking setup question rather than a SIP specific question... We are also a triple play provider using Calix, but our phone lines are provided by a Meta softswitch. I am a network engineer on the VoIP side, and do double duty on our Mitel PBX's
In this case, your Calix voice network should be isolated from your Mitel network, and you should be able to serve the DHCP for the Calix side from your Calix host or third party server, you would then want an SBC sitting on the network edge of your Mitel, whether that is a MBG, Acme Packet, Sansay, Adtran, or something else to act as your proxy. You setup your ports on your Calix to register to the SBC, which handles the translation to talk to the Mitel.
My question is what are you hoping to gain by doing this way vs using a softswitch for the dial tone? What scale are you looking at here, because getting beyond a few hundred SIP stations on the Mitel can produce some challenges and you have to decide is the licensing is worth it, or if you should be looking at a more at softswitch.