I think there is a mental shift that needs to happen. Men aren't "helping" or "supporting" their wives. They are equally responsible for what happens in the home. You can see this illustrated by a woman saying, "I'm helping my husband by doing the dishes." We inherently understand that by saying "help" they aren't taking responsibility for the task.
When men see themselves as equal partners in the home they will no longer say they are helping nor babysitting, they will say they are taking care of the home and raising their children.