Is it possible to set the stacking order of pseudo-elements below their parent element?

Pseudo-elements are treated as descendants of their associated element. To position a pseudo-element below its parent, you have to create a new stacking context to change the default stacking order.
Positioning the pseudo-element (absolute) and assigning a z-index value other than “auto” creates the new stacking context.

#element { 
    position: relative;  /* optional */
    width: 100px;
    height: 100px;
    background-color: blue;
}

#element::after {
    content: "";
    width: 150px;
    height: 150px;
    background-color: red;

    /* create a new stacking context */
    position: absolute;
    z-index: -1;  /* to be below the parent element */
}
<!DOCTYPE html>
<html>
<head>
  <meta charset="utf-8">
  <title>Position a pseudo-element below its parent</title>
</head>
<body>
  <div id="element">
  </div>
</body>
</html>


I know this is an old thread, but I feel the need to post the proper answer. The actual answer to this question is that you need to create a new stacking context on the parent of the element with the pseudo element (and you actually have to give it a z-index, not just a position).

Like this:

#parent {
    position: relative;
    z-index: 1;
}
#pseudo-parent {
    position: absolute;
    /* no z-index allowed */
}
#pseudo-parent:after {
    position: absolute;
    top:0;
    z-index: -1;
}

It has nothing to do with using :before or :after pseudo elements.

#parent { position: relative; z-index: 1; }
#pseudo-parent { position: absolute; } /* no z-index required */
#pseudo-parent:after { position: absolute; z-index: -1; }

/* Example styling to illustrate */
#pseudo-parent { background: #d1d1d1; }
#pseudo-parent:after { margin-left: -3px; content: "M" }
<div id="parent">
 <div id="pseudo-parent">
   &nbsp;
 </div>
</div>


Try it out

el {
  transform-style: preserve-3d;
}
el:after {
  transform: translateZ(-1px);
}