Ah, interesting points
Lachwen. However, Tolkien's exact words were that there were three unions of the Eldar and the Edain. Now, the Eldar were originally the name of
all Elves, but then only those who made the Great Journey to Valinor were known as Eldar afterwards. Thus, Nimloth was not of the Eldar. Also, while Dior was mortal (due to Manwe's decree), he was not fully mortal and was only half-Edain. Therefore, Dior was not of the Edain so it was simply the union between an Elf and a half-mortal, quarter-Ainu, quarter-Elf; that's Dior by the way!
In the case of Imrazor and Mithrellas, Mithrellas was a Silvan Elf and not of the Eldar and so for the same reason their marriage was not a union between the
Eldar and the
Edain, even though Imrazor was of the Edain, being Numenorean. So, yes, there
are four unions between Elves and Men, but only three of them were unions between the Eldar and Edain- that is, Tuor and Idril, Beren and Luthien and Aragorn and Arwen- so the Professor remains both a master of words and by the look of this question, he would make a pretty good riddle-writer also
.