The solution by PeterVR has the disadvantage that the additional color displays on top of the entire HTML block - meaning that it also shows up on top of div content, not just on top of the background image. This is fine if your div is empty, but if it is not using a linear gradient might be a better solution:
<div class="the-div">Red text</div>
<style type="text/css">
.the-div
{
background-image: url("the-image.png");
color: #f00;
margin: 10px;
width: 200px;
height: 80px;
}
.the-div:hover
{
background-image: linear-gradient(to bottom, rgba(0, 0, 0, 0.1), rgba(0, 0, 0, 0.1)), url("the-image.png");
background-image: -moz-linear-gradient(top, rgba(0, 0, 0, 0.1), rgba(0, 0, 0, 0.1)), url("the-image.png");
background-image: -o-linear-gradient(top, rgba(0, 0, 0, 0.1), rgba(0, 0, 0, 0.1)), url("the-image.png");
background-image: -ms-linear-gradient(top, rgba(0, 0, 0, 0.1), rgba(0, 0, 0, 0.1)), url("the-image.png");
background-image: -webkit-gradient(linear, left top, left bottom, from(rgba(0, 0, 0, 0.1)), to(rgba(0, 0, 0, 0.1))), url("the-image.png");
background-image: -webkit-linear-gradient(top, rgba(0, 0, 0, 0.1), rgba(0, 0, 0, 0.1)), url("the-image.png");
}
</style>
See fiddle. Too bad that gradient specifications are currently a mess. See compatibility table, the code above should work in any browser with a noteworthy market share - with the exception of MSIE 9.0 and older.
Edit (March 2017): The state of the web got far less messy by now. So the linear-gradient
(supported by Firefox and Internet Explorer) and -webkit-linear-gradient
(supported by Chrome, Opera and Safari) lines are sufficient, additional prefixed versions are no longer necessary.