The answer depends on whether or not your other elements are descendants of the containerDiv or not. To answer the question: Yes, it's almost certainly possible, given a bit of shuffling of the markup.
But what you need to understand is the concept of stacking context:
http://www.w3.org/TR/CSS2/visuren.html#layers
Stacking context is not inherited the way other properties are: "A stacking context is atomic from the point of view of its parent stacking context; boxes in other stacking contexts may not come between any of its boxes." It's not like every element on the page with z-index:2
will be behind everything on the page with z-index:4
. Z-index (combined with a position declaration) is typically (though not exclusively) used to resolve the stacking order when two elements share a containing element.