You ne peut pas really do this. Your card seulement has one MAC address mais multiple IP interfaces. They will need to have leur addresses statically assigned.
When le DHCP server sends back le DHCPOFFER how does it get delivered to eth0:1 et pas to eth0? eth0:1 sends out a DHCPDISCOVER ou a DHCPREQUEST by broadcasting. The DHCP server responds avec a DHCPOFFER to inform le client of its IP address. But how will le DHCPOFFER arrive si eth0:1 ne yet have an IP address? The DHCP server broadcasts back et relies on le link layer to correctly deliver le ethernet frame (with le autre associated layers stacked on top of it) to le right MAC address. And now votre device has an IP address.
The problem for le DHCPOFFER is that depuis a Layer-2 perspective le two "devices" (eth0 et eth0:1) are indistinguishable, et so (from a Layer-3 perspective) le DHCPOFFER is destined for 255.255.255.255 (because eth0:1 ne yet have an IP address).
Vous pouvez get around this by using VLANs. VLANs will allow you to take le même physical broadcast domain et treat it like multiple "virtual" broadcast domains (hence le name).