In Unfinished Tales, the wicked Easterling Brodda forces the Edain woman Aerin to marry him, but he is eventually killed by Turin, a kinsman of Aerin, in revenge for the Easterlings' oppression of the Edain. Aerin then burns Brodda's hall in her final act of resistance against the Easterlings.
Appendix A of the LOTR describes the killing of Freca, a chieftain in Rohan, by his liege lord, King Helm of Rohirrim, for daring to ask for the king's daughter's hand in marriage for his son. The justification for the murder is the uppity aspirations of the insubordinate vassal. But it is also mentioned that Freca had "much Dunlendish blood and was dark-haired" - in other words, he is in part descended from a race which is not on the "good" side, and this fact seems to overshadow his Edain heritage. While it is not explicitly stated that Freca's coarse, evil personality comes along with his blood lineage, Tolkien does on more than one occasion, mention racial heritage hand in hand with character.
But if the lesser race in question is the Edain, and the higher race is the Elves, these rules can be bent. The Elf King Thingol did try to kill the human Beren for asking for Thingol's daughter's hand. But eventually, Thingol realizes that Beren is worthy, and approves the marriage. And the human Tuor encountered no resistance at all from Idril's father when he asked for the Elf princess in marriage.
ROTK mentions Imrahil the Prince of Dol Amroth. Legolas recognizes the human prince as part-Elvish and accords special honor to him. Unfinished Tales mentions the genealogy of the lords of Dol Amroth:
"...Angelimar was the twentieth in unbroken descent from Galador, first Lord of Dol Amroth... Galador was the son of Imrazor the Numenorean, who dwelt in Belfalas, and the Elven-lady Mithrellas... it was ever held that the house and kin of the Lords of Dol Amroth was noble by blood as they were fair in face and mind."
Once again, we see the idea of "biology=destiny". That a genetic contribution from a 'higher' race can endow one with mental and physical 'superiority'. One need not look too hard in the real-world to find the equivalent of this ideology: the mixed children of whites and non-whites are often regarded as being of "higher status" than full-blooded non-whites. This is expressed in the racial classifications of old Mexico, the "good hair", "pale eyes" and "light skin" standard of beauty among black Americans, and the adoration of the Eurasian in many Asian circles.
Between LOTR, UT, and The Silmarillion, there are altogether 4 Elf-woman/human-man couples - Arwen/Aragorn, Idril/Tuor, Luthien/Beren, Mithrellas/Imrazor. There are, however, no Elf-man/human-woman couples, except for the case of Aegnor and Andreth mentioned in The Histories of Middle Earth, but they did not marry or leave offspring. In contrast, all four Elf-woman/human-man couples proved fruitful and gifted the world with brilliant descendents. Why is there such a double standard? I believe it is purely due to a sexist world view: an aging, ugly man can have a young-looking, beautiful wife, but an aging, ugly woman does not deserve a youthful-looking, beautiful husband. Such views are not unique to Western Europe. Other cultures also have folklore of immortal women marrying mortal men, while tales of the reverse are conspicuously absent.
While human+Elven mixing is always described in positive terms, human+human mixing is not seen as a good thing. Mixing with a "lesser" race results in a predisposition towards weakness. One might argue that perhaps the Edain were honored for their wisdom in choosing good over evil, and their strength in battling the devil, not for their racial makeup, but in Tolkien's universe, wisdom, strength, and race seem to go hand in hand. The Numenoreans, descendants of the Edain, returned to Middle Earth, and the last chapter of The Silmarillion tells of their fate:
[Note: Gondor was one of the kingdoms established by the Numenoreans. Mordor was the stronghold of Sauron, servant of Morgoth the devil.]
Yet at the last, in the wearing of the swift years of Middle-earth, Gondor waned, and the line of Meneldil son of Anarion failed. For the blood of the Numenoreans became much mingled with that of other men, and their power and wisdom was diminished, and their life-span was shortened, and the watch on Mordor slumbered.
So here we see social disintegration goes together with intermarriage with "inferior" races. There are more accounts that imply that mixing with a less "upright" race results in predisposition towards allying with evil. In the Notes to the chapter "The Battles of the Fords of Isen" in Unfinished Tales, mention is made of the people who lived between Isen and Adorn. Their land was "nominally" part of Rohan, and the inhabitants "were largely of mixed blood" - Dunlendish and Gondorian - a non-Edain + Edain mix. According to UT, "they were more disposed to side with Saruman, and many of their warriors had joined Saruman's forces. In their choice to fight on the "evil" side, rather than on the side of Rohan, these mixed folk follow their non-Edain ancestors, being "more friendly disposed towards the Dunlendings than to the 'wild Northmen' who had usurped the land, the wild Northmen being the Rohirrim, which came from Edain stock.
There is a view among some people that mixed-race individuals are "corrupted" by the "lower" part of their heritage. And Tolkien's descriptions of humans of mixed heritage seem to support that line of thinking, except for those humans who were of mixed human and Elven heritage.