Actually, in another instance, Tolkien said this in
Letter No. 153.
Quote:
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Elves and Men are evidently in biological terms one race, or they could not breed and produce fertile offspring – even as a rare event: there are 2 cases only in my legends of such unions, and they are merged in the descendants of Eärendil.
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This letter was written in September 1954 - *after*
The Lord of the Rings was published (which included the statement about 'three unions'). I find this quote to be most sufficient in explaining the reality of the situation - Arwen was not an Elf, Dior was not entirely a Man, and Mithrellas' story was not presented in his legend (though it was hinted at when Legolas recognizes the elvish strain in Imrahil). Mithrellas' case certainly does count as a man-elf union, but Tolkien had no idea that it would ever be revealed to the public.
"Elves and Men are evidently in biological terms one race, or they could not breed and produce fertile offspring"
Dior and Arwen are products of these unions; their unions do not really fall under the category of man-elf unions for the blood of both men and elves already flow in each. In short, 'unions of man and elf' and 'unions of mortal and immortal' are different things.