I looked up "half duplex" out of interest, and it fit closely enough what I imagined it meant. But the first article I found says that cell phones are full duplex. However I've found they have a threshhold volume under which they don't send any signal to the other party, so perhaps that can make it feel like half duplex. Am I misunderstanding this?
I think you are right. During my search prompted by your question I also found many complaints about phones acting as if they are half duplex though. Variously attributed to echo cancellation, low quality phones, low quality service, etc.
Link: http://electronics.howstuffworks.com/cell-phone1.htm