The other odd thing about placenta: "The placenta is unique in that it is an organ which arises from the tissue of two genetically distinct organisms; part of the placenta develops from the tissue of the mother’s uterine wall, while another part develops from the fetus’ own tissue. After the blastocyst which will develop into the fetus makes contact with the uterine wall, blastocyst and maternal tissue grow together to form a single, cooperating organ that links the two together."

I don't know whether mothers think of the placenta as their own body part or part of the baby, but personally I think it is in poor poor taste to eat baby parts.