Relationships between Female Characters of Different Races
Apparently there are a plethora of interracial relationships in the Legendarium, especially between male characters, but there are also prominent interactions or important relationships between male characters and female characters aside from romance. In terms of relationships between female characters of different races, we have:
Therefore she went to the doors of the House of Vairë and prayed to be admitted; and this prayer was granted, although in that House none of the Living dwelt nor have others ever entered it in the body. But Míriel was accepted by Vairë and became her chief handmaid; and all tidings of the Noldor down the years from their beginning were brought to her, and she wove them in webs historial, so fair and skilled that they seemed to live, imperishable, shining with a light of many hues fairer than are known in Middle-earth. This labour Finwë is at times permitted to look upon.
- Morgoth's Ring: The Statue of Finwë and Míriel
Yet Galadriel his sister dwelt never in Nargothrond, but remained in Doriath and received the love of Melian, and abode with her, and there learned great lore and wisdom concerning Middle-earth.
- The War of Jewels: Of Men
1. They came at last to Húrin’s house, and when Morwen learned that Túrin was received with honour in the halls of Thingol her grief was lightened; and the Elves brought also rich gifts from Melian, and a message bidding her return with Thingol’s folk to Doriath. For Melian was wise and foresighted, and she hoped thus to avert the evil that was prepared in the thought of Morgoth. But Morwen would not depart from her house, for her heart was yet unchanged and her pride still high; moreover Niënor was a babe in arms. Therefore she dismissed the Elves of Doriath with her thanks, and gave them in gift the last small things of gold that remained to her, concealing her poverty; and she bade them take back to Thingol the Helm of Hador. But Túrin watched ever for the return of Thingol’s messengers; and when they came back alone he fled into the woods and wept, for he knew of Melian’s bidding and he had hoped that Morwen would come. This was the second sorrow of Túrin. When the messengers spoke Morwen’s answer, Melian was moved with pity, perceiving her mind; and she saw that the fate which she foreboded could not lightly be set aside.
2. Then Melian, who had remained silent, spoke: ‘Go not hence, Morwen. A true word you said: this doubt is of Morgoth. If you go, you go at his will.’
1. There Valandil, Lord of Andúnië and close kin of Aldarion, held a great feast; and at that feast he drank to Erendis, naming her Uinéniel, Daughter of Uinen, the new Lady of the Sea. But Erendis, who sat beside the wife of Valandil, said aloud: ‘Call me by no such name! I am no daughter of Uinen: rather is she my foe.’
2. ‘I will not share my husband with the Lady Uinen,’ said Erendis.
- Unfinished Tales: Aldarion and Erendis
Half-Elf(mortal woman at this point) and Hobbit
1436 King Elessar rides north, and dwells for a while by Lake Evendim. He comes to the Brandywine Bridge, and there greets his friends. He gives the Star of the Dúnedain to Master Samwise, and Elanor is made a maid of honour to Queen Arwen.
- Appendix B: The Tale of Years
So, there is a lack of relationship between elven women/human women/dwarven women, and that's where our headcanons come in.