Cells of umbilical cord - mom's or son's?
Cells of umbilical cord - mom's or son's?


Answer: Son's. 

The interface you are looking for is in the placenta. https://en.wikipedia.org/wiki/Placenta

Formally the fetal side of the placenta is called the Chorion frondosum, which develops from the outer cells of blastocyst (trophoblast), and the maternal side of the placenta, Decidua basalis, which develops from the maternal uterine tissue.


  How is it even possible?


Immune tolerance in pregnancy or gestational/maternal immune tolerance

The placenta functions as an immunological barrier between the mother and the fetus, creating an immunologically privileged site. For this purpose, it uses several mechanisms


It secretes Neurokinin B containing phosphocholine molecules. This
is the same mechanism used by parasitic nematodes to avoid detection
by the immune system of their host.
Also, there is the presence of small lymphocytic suppressor cells in the
fetus that inhibit maternal cytotoxic T cells by inhibiting the
response to interleukin 2.
The placental trophoblast cells do not express the classical MHC
class I isotypes HLA-A and HLA-B, unlike most other cells in the
body, and this absence is assumed to prevent destruction by maternal
cytotoxic T cells, which otherwise would recognize the fetal HLA-A
and HLA-B molecules as foreign. On the other hand, they do express
the atypical MHC class I isotypes HLA-E and HLA-G, which is assumed
to prevent destruction by maternal NK cells, which otherwise destroy
cells that do not express any MHC class I. However, trophoblast
cells do express the rather typical HLA-C.
It forms a syncytium without any extracellular spaces between cells
in order to limit the exchange of migratory immune cells between the
developing embryo and the body of the mother (something an
epithelium will not do sufficiently, as certain blood cells are
specialized to be able to insert themselves between adjacent
epithelial cells). The fusion of the cells is apparently caused by
viral fusion proteins from endosymbiotic endogenous retrovirus
(ERV). An immunoevasive action was the initial normal behavior of
the viral protein, in order to avail for the virus to spread to
other cells by simply merging them with the infected one. It is
believed that the ancestors of modern viviparous mammals evolved
after an infection by this virus, enabling the fetus to better
resist the immune system of the mother.


Other mechanisms include exposure to immune modulating factors present in seminal fluid from vaginal and oral sex. https://en.wikipedia.org/wiki/Pre-eclampsia#paternal_tolerance