TL;DR:
Some of the Valar are described in the Silmarillion as husband and wife, and others are described as siblings. But it seems that the Ainur don't procreate, and it's unclear what marriage means between Valar because the only example of husband and wife about which we learn anything (Aulë and Yavanna) isn't really an affectionate one.
Has Tolkien ever explained how he conceives these family relations between the Valar?
Overly-long elaboration on my thoughts on the matter
While listening to a Silmarillion audio book the other day (the Valaquenta and the first chapters of the Quenta Silmarillion specifically), I stumbled across something that I never really thought about before. The Silmarillion describes some family relations between some of the Valar. For example, Mandos, Lórien, and Nienna were siblings as were Nessa and Oromë, Vairë was the wife of Mandos, Yavanna was the wife of Aulë, and Varda was the wife of Manwë.
Among the Elves and Men, brothers and sisters are individuals with the same parents. A wife and a husband are two individual Elves or Men that live in a close, voluntary, and exclusive partnership that typically involves affection (but that doesn't have to be so, as the Eöl-Aredthel relation shows – somewhat surprisingly, the validity of the marriage isn't challenged by Turgon if I remember correctly). I can't think of an instance in the Silmarillion in which a child is born to parents who are not wife and husbands, so procreation seems to be linked to wedlock as well.
But it occurred to me that I have no idea what these terms – brother, sister, wife, husband – mean in relation to the Valar. I don't think that there's any report of a Vala or Maia having parents (unless in a metaphorical sense in which Eru is the father of all Ainur). Conversely, I think Melian is the only Ainu that has ever given birth to a child, but since she's married to an Elf, it seems fairly safe to assume that the Ainur don't procreate. So in what sense can Mandos, Lórien, and Nienna be described as siblings, then?
As to the marriages between the Valar, what does this status actually mean? Unlike among the Elves and Men, it doesn't entail procreation¹, and the described married couples are never shown to feel a strong affection for each other. While some of them appear to live together (Manwë and Varda in Ilmarin, Mandos and Vairë in the Halls of Mandos), that's not always the case as Aulë and Yavanna don't appear to have such a shared residence.
The latter example is interesting because the most detailed description of an interaction between two married Valar is found in the chapter "Of Aulë and Yavanna". Aulë decides to keep the creation of the Dwarves secret at first, but later chooses to confide to Yavanna. But there isn't any trace of mutual understanding between the two. On the contrary, there is something close to an argument because Yavanna predicts that the Dwarves wouldn't care at all about the things in her domain, which doesn't seem to bother Aulë at all. Eventually, she agrees with Manwë (one might say, behind Aulë's back) to ensure that at least the forests are protected from Aulë's creation. She then returns to him and tells him in a way that might be described as sneeringly that she's managed to score at least a small victory against him. This interaction could have taken place just as well between two Valar who are not husband and wife, and it's a far cry from some of the more affectionate marriages among the Children of Ilúvatar.
As all this made less and less sense to me, I tried to frame the relations between the Valar in terms of the different types of love from Ancient Greek, and this kind of works. The feeling between two Valar who identify as wife and husband might be similar to Greek agapé (the emotion you feel toward your children and your spouse), whereas the feeling between Valar who identify as siblings might be related to Greek philia (the special type of loyality reserved for family members, your friends, and members of your community). The emotion between married Elves and married Men might then perhaps be described as éros (which includes sexual passion).
Basically, this assumes that there are different types of emotion between the Valar: some feel agapé for each other, and the narrative voice of the Silmarillion chose the terms "husband" and "wife" in that case. Others feel philia, and the words to describe this feeling were "brother" and "sister". This appears to work at least to some degree. I assume that with his education in classics, Tolkien was well aware of this philosophy of love. But is there any hint in his writing of how he really conceived the relations between the Valar? Did he ever explain why some Valar were considered siblings, and what a wedlock between Valar actually meant?
¹ It might still entail sexual attraction and intercourse, of course.
