The children are NOT shielded from what's going on. Many of us here were/are children of alcoholic parents, and fights are only one part of the dysfunction that harms them. Having a parent who isn't present, who can't be counted on, who does or says embarrassing or hurtful things--those all affect kids negatively.
Most alcoholics aren't terrible people. But being someone who doesn't lie or steal isn't much qualification to be a partner or a parent. I understand loving one's partner, even as you are watching their lives circling the drain. But the thing about drowning partners is that if you don't let go, you get dragged down with them.
If you stay together, PLEASE get the kids some help. Depending on their ages, Alateen is available. School counselors are another good resource. One of the very worst things that can happen in an alcoholic household is that everybody covers up the "big secret"--it's very damaging to the kids and is yet another form of enabling.