Are radio channels used by airliners half-duplex channels? Can a pilot transmit and receive information at the same time? Or can he either transmit or receive but not at the same time?

I thought communication channels were half-duplex because this reduced the chance of the information by trasmitter (say the ATC) being overlapped by information from the receiver (the pilot) in case he possibily accidentaly pressed the PTT button. Is that a right assumption or not?
They are half-duplex because all parties share the same frequency. Only one party can transmit at any time.

Full duplex would require two frequencies and therefore third parties would have to monitor both frequencies simultaneously in order to hear both sides of the conversation. Half-duplex operation on a single frequency is inherently 'open-channel' - everybody can hear everything transmitted by anybody else on that frequency. That's the way it's always been done in aviation and in many other fields.

(Answer taken from comments by https://aviation.stackexchange.com/users/13124/transistor and https://aviation.stackexchange.com/users/15152/fiddlesticks)