Let's say we have a mother giving a birth to a son. In a very clear manner the cells of these two individuals are very different, of course. Yet there is an umbilical cord connecting them. Then there should be a clearly defined "border" somewhere on its way where the mother's cells meet the cells of her son, is that so? How is it even possible?! ;)
Cells of umbilical cord - mom's or 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