No, it’s not possible I’m afraid. There was talk of a ::contains pseudo class but it was dropped.
At present css only works one way and you can’t find something then work back up and style the parent.
The parent selector has been asked for many times but is something that would be very awkward to achieve due to the way that css works.
Depending on your situation you could probably fake something by using the :before or :after pseudo classes to add some content to provide a background to the div but would be pretty reliant on structure.
Here is an example that will work in IE8+ but is reliant on a certain structure.
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Untitled Document</title>
<style type="text/css">
.outer {
position:relative;
width:50%;
background:red;
z-index:-2;
padding:10px;
}
.highlight:after {
content:" ";
position:absolute;
z-index:-1;
top:0;
left:0;
right:0;
bottom:0;
background:green
}
span {
background:blue;
color:#fff
}
</style>
</head>
<body>
<div class="outer">
<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis pellentesque mauris pellentesque justo congue in faucibus justo faucibus. Nunc odio sapien, vehicula eget interdum quis, euismod dignissim magna. Morbi condimentum massa sit amet nisl fringilla quis laoreet sapien porttitor. Aenean adipiscing rutrum accumsan. Cras ipsum ligula, pretium sit amet fermentum et, viverra quis quam. Suspendisse sed lacus augue, a sagittis metus. Nunc pulvinar, <span class="highlight">Green Background added </span>, enim orci viverra dui, at iaculis quam odio sit amet eros. Aliquam eleifend ipsum et libero sollicitudin dictum eu et ipsum. Phasellus venenatis semper felis, vitae pretium enim fermentum lacinia. Nulla a erat tortor, et fermentum nisi. Suspendisse potenti. Ut pellentesque lorem ut metus convallis viverra. Nam sagittis, mauris sit amet tempor viverra, orci odio condimentum mi, eu semper metus odio vel augue. Nunc diam quam, cursus quis mollis a, rutrum euismod nisl. </p>
</div>
<div class="outer">
<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis pellentesque mauris pellentesque justo congue in faucibus justo faucibus. Nunc odio sapien, vehicula eget interdum quis, euismod dignissim magna. Morbi condimentum massa sit amet nisl fringilla quis laoreet sapien porttitor. Aenean adipiscing rutrum accumsan. Cras ipsum ligula, pretium sit amet fermentum et, viverra quis quam. Suspendisse sed lacus augue, a sagittis metus. Nunc pulvinar, <span>Original Red background shows through</span>, enim orci viverra dui, at iaculis quam odio sit amet eros. Aliquam eleifend ipsum et libero sollicitudin dictum eu et ipsum. Phasellus venenatis semper felis, vitae pretium enim fermentum lacinia. Nulla a erat tortor, et fermentum nisi. Suspendisse potenti. Ut pellentesque lorem ut metus convallis viverra. Nam sagittis, mauris sit amet tempor viverra, orci odio condimentum mi, eu semper metus odio vel augue. Nunc diam quam, cursus quis mollis a, rutrum euismod nisl. </p>
</div>
</body>
</html>
The background of the parent div is only green when there is a child with a classname of .highlight.