I consider a one parent family, where there are two parents but one of them no longer wants to remain in the original family, to be a broken home even if the single parent manages to make that home a good place. I think for children their parents splitting up is a horror, the nightmare they hoped wouldn't be their family. I do believe they will always have scars from this.
However, once the family is split up, I think one good parent can make a very safe home for the children. I agree with what Anjae wrote, home being a good safe place for the kids, where they know they can ask questions, where although the left behind parent will not be creating a fake innocent image of the parent who left, the kids know that their father (in my case) is still loved.
Kids like predictability, it makes them feel safe. I believe that in spite of a broken home, it is a good lesson for the kids if the left behind parent can go on an create a cosy home where there is laughter and kindness and nurturing. They are watching us, and how we react to everything will probably have a huge effect on how they absorb what has happened to their family.