After every birth I assist in I ask the couple if they would like to look at the placenta and if they do I go through it all with them what it does etc. .
I had a good look at both ds's and dd's placentas, with the mw running me through what all the different bits were and did. It was fascinating (especially the second time when i wasn't stoned to the eyeballs) and I'd highly recommend it- even if it did, quite literally, make dh vomit