Not sure if it's the most elegant solution to your problem, but using div to group div in row, I was able to sort the odd and even row, and apply style to their odd or even child.
Take a look here : http://jsfiddle.net/3ASE8/
#div_parent {
width: 500px;
}
.child {
display: inline-block;
margin: 5px;
width: 100px;
height: 100px;
line-height: 100px;
text-align: center;
background-color: #333;
color: red;
}
.row:nth-child(odd) .child:nth-child(even) {
background-color: #ccc!important;
}
.row:nth-child(even) .child:nth-child(odd) {
background-color: #ccc!important;
}