Beagle,
As I understand you, you have two physically separate phones (not a common base station with 2 remotes), so that is a different scenario to ChristiaanJ.
A single DECT phone cannot (
AFAIK) support multiple handsets both transmitting and receiving concurrently, although simultaneous receiving is possible (as ChristiaanJ mentions). I think it's analagous to VHF radio comms - only one station can transmit, but anyone in range can receive.
In answer to ChristiaanJ's original Q, I see no reason why two distinct and separate DECT phones with independent base stations should not work simultaneously in the desired fashion - although you would need to check that they don't operate on the exact same frequency and interfere with each other.
SD