To achieve what you want without removing any styles you have to make the z-index of the '.parent' class bigger then the '.wholePage' class.
.parent {
position: relative;
z-index: 4; /*matters since it's sibling to wholePage*/
}
.child {
position: relative;
z-index:1; /*doesn't matter */
background-color: white;
padding: 5px;
}
jsFiddle: http://jsfiddle.net/ZjXMR/2/