Cloud and Tifa act as surrogate parents. Marlene isn't Barret's daughter by blood either, and so by the point in the game, it is pretty clear she looks to Barret like a father and Tifa as something of a mother. Since Barret is gone a lot in the events leading up to Advent Children, she is left in Cloud and Tifa's care.
You could say that much of the story of Advent Children is the story of surrogate families. Although not related by blood, Denzel and Marlene are Cloud and Tifa's family, just like Cid, Yuffie, Red XIII, Barret, Cait Sith, and Barret are all "dear friends"...like a family, really.