The definition of a rainbow family states that at least one parent is homosexual.
At this point, associations quickly arise of two women married to each other who have started a family by means of sperm donation. Or the gay couple who hired a surrogate mother abroad. Certainly, this is the majority of constellations. But a rainbow family can be much more.
Lesbian women and gay men can also come together and start a family together, there are quickly more than two adults together and the term rainbow family could be expanded to include multi-parenthood. In this case, the constellation could also be co-parenting, because the lesbian woman and the gay man are not a romantic couple.
It becomes more complex when people who have different sexual orientations now come together as a family. For example, a straight woman and a gay man couple. This would also be a rainbow family, but at the same time they would also be co-parenting and the single woman would be a solo mother in co-parenting.
And to complicate it further, there could be a pre-existing heterosexual marriage where the man is infertile and those spouses seek out a gay man to join them in family life. Strictly speaking, this would also be a rainbow family.