[Son of Númenor]

For of the Maiar many were drawn to his splendour in the days of his greatness, and remained in that allegiance down into his darkness; and others he corrupted afterwards to his service with lies and treacherous gifts. Dreadful among these spirits were the Valaraukar, the scourges of fire that in Middle-earth were called the Balrogs, demons of terror. (Valaquenta)

And in Utumno he gathered his demons about him, those spirits who first adhered to him in the days of his splendour, and became most like him in his corruption: their hearts were of fire, but they were cloaked in darkness, and terror went before them; they had whips of flame. Balrogs they were named in Middle-earth in later days. And in that dark time Melkor bred many other monsters of divers shapes and kinds that long troubled the world; and his realm spread now ever southward over Middle-earth. (Quenta Silmarillion, "Of the Coming of the Elves and the Captivity of Melkor")

I can't recall Balrogs ever being referred to as the 'Children of Melkor.' Tolkien was very careful about his word choice, and I can't see him using the word 'children' (which has specific divine [e.g. Children of Iluvatar, Children of Aule] or biological denotations in his writing) to describe the servants of a being who is described as barren and incapable of creation.