Q.  Thanks for your answer. Here is another question:
I wanted to have a home birth with a midwife until she told me that the practice suggests putting the afterbirth in the freezer until burial. This seemed disgusting to me so I  decided to go to the hospital. However, I was wondering what is the halacha regarding this matter since it contains blood and other tissues. I was talking to a friend and she told me that some goyim eat it or turn it into vitamin pills since it supposedly had curative properties. Once again, I found this unappetizing to say the least and somehow suspect that it is against Halacha. Please let know.
Kol tuv.
A. Although some Poskim maintain that the ‘Shilya’ or afterbirth should be buried, (Sdei Chemed – Kuf 37, quotes Nechmad Lemareh, following Talmud Yerushalmi – Shabbos 18: 3). Most Poskim do not require burial and the afterbirth can be just discarded. (Tzitz Eliezer 10: 55, Shivtei Yisroael 2: 29: 15, Gesher Hachayim 1: 16 and others). It is not customary to do burial in our days, however, there are diverse minhagim.
Regarding your second issue, in question 1491 we received the following: “There is an ancient (non-Jewish) tradition which has become popular among new moms, placenta ingestion. Moms report that they have less post postpartum depression, increased energy and milk production. Is a human placenta kosher, what about the placenta of kosher animals?
To what we answered: Placentophagia or the act of mammals eating the placenta of their young after childbirth, when done by humans, besides kashrus concerns, also presents health issues, as it could become easily contaminated by the lack of refrigeration and septic concerns. (See; Risks of eating the placenta at parents.com). The benefits are also questionable. (See; Should I eat my placenta, at webmd.com).
In regards to the kashrus of the afterbirth or shilya, if it was delivered by a kosher live animal that gave birth, it would be prohibited as being; yotze min hachai or a derivative from a live animal . (Chulin 77a, Rambam – Macholos Asuros 5: 13, Kaf Hachaim Y.D. 81 34). If the animal underwent proper shechita and the placenta was found inside, it would be permitted.
In regards to a human placenta, Rema (Y.D. 79: 1) rules like Rambam that, “It is Biblically forbidden to eat human flesh.” Although many Poskim adopt Rema’s strict ruling, some others maintain that the matter is unresolved or even rule like the Rishonim who are Biblically lenient, but still Rabbinically prohibited (see Taz YD 79:3, Pri Hadash 79:6, and Darkei Teshuvah 79:15).
Therefore, Horav Shlomo Miller’s Shlit’a opinion is to avoid human placentophalagia.
(Interestingly, the Torah mentions placentophalagia as part of the curses of the tochacha. Devarim 28: 57).”
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a.