You can't. You'll need to super-impose (positioning, and z-index) the children over the parent, meaning they will no longer be children. That, or use transparent png's for the parent background, and set opacity for any siblings of the fully-opaque child.
*untested, but should be good.
.signup_backdrop {
position:fixed;
top:0; left:0;
background:#333333;
width:100%; height:100%;
z-index:10;
}
.signup_box {
position:fixed;
top:25%; left:25%;
background:#ffffff;
width:50%; height:50%;
z-index:20;
}
<div class="signup_box">
<p>Hello World</p>
</div>
<div class="signup_backdrop"></div>