Have you considered somatic cell nuclear transfer aka cloning? No need for sex cells from two mortals, just take a mortal egg cell, remove nucleus and replace it with a nucleus from an immortal somatic cell. The capability to use this technique of course depends on the scientific level of your immortals, we humans have so far only cloned Dolly the Sheep and some macaques. Also, cloning of humanoids might be a moral issue.
Second thing that came to mind reading your question is the viability of immortals to be surrogates. Lacking the ability to produce sex cells, why would female immortals have a menstrual cycle or even any capability to form uteral lining to grow a fetus? This is something you might want to consider.
Considering your question aka how can a surrogate mother give the fetus she is carrying her immortality. As previously @Willk has pointed out, microchimerism is known to happen both fetal to mother and mother to fetus in placental mammals, including humans. However, little is yet known about this phenomenon. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5532073/ This article might be a heavy read, but the key points in the end summarise it nicely. (The article also touches the issue of immune tolerance in expecting mothers, which might also be of interest to you considering your surrogate mother carrying a different species, but this was not the question). The conclusion is that we don't know what types of cells are passed on to the fetus during pregnancy. After quickly glancing over a few other abstracts on the matter, the scientific evidence seem to point to the conclusion that mother to fetus microchimerism happens to help the child's immune system mature into something more complex than it would without this phenomenon (sorry, english third language). For me, as a person who likes to pretend to know something about human biology and immunology, it seems like a little bit of a stretch to think that the surrogate mother could pass on stem cells to the fetus it's carrying, and that the stem cells could replace all the cells of a fetus without causing a immune reaction and downright rejection by the child's immune system. But, we also have a story with immortals and as I said, the research is incomplete, so what the hell.
However, while researching this, I also came across the info that different types of immune cells are passed on to a baby during breastfeeding... at least in mice. So I thought that if you formed your reason for the immortals' immortality around their different immune system, you could explain that the effect of the surrogate mother on the child's immune system both during pregnancy and while breastfeeding would compound into the child getting immortality through immortal-like immune system. This system could also cause a different level of immortality.
- maternal microchimeric stem cells in fetus/child somehow evading immune system and replacing all other cells over time
- immortality because of immune system + motherly effect on child's immune system during pregnancy, breastfeeding (and a tad growing up)
I hope I didn't fall to much into the realm of discussion, I'm new to this website. :)