>Conventional stereo doesn't include those details. Alternative systems like Ambisonics do.
Ears don't hear up/down and front/back. Ears hear left and right. The _brain_ uses information from tiny deviations of the sound which are caused by your head being in the way and then decodes it as being up/down and front/back.
This is what binaural sound is about, meaning, if you record in stereo something using earplug microphones, then listen to that recording using earplug headphones, those tiny deviations are present in that stereo recording and it'll cause your brain to determine the position of the sound source using that information. It's a psychoacoustic effect, like the reverb tells our brain the room characteristics a sound is played in. We don't actually need to be inside that room to playback a sound, we just add the reverb, the effect is good enough for our brains.
To me, the whole surround audio for consumers is a marketing gimmick because you can never get good enough and they can always keep selling newer and bigger speaker setups. The only adequate setup would be an anechoic spherical room, you sitting at the center and speakers in every direction possible. Surround as it is now has some practical use in motion pictures and mostly cinemas, to give you a somewhat feeling you're in the action, but it's not actually proper surround.