If you don't mind using absolute positioning, you can position your background image, and then add an overlay using opacity.
div {
width:50px;
height:50px;
background: url('http://images1.wikia.nocookie.net/__cb20120626155442/adventuretimewithfinnandjake/images/6/67/Link.gif');
position:absolute;
left:0;
top:0;
}
.overlay {
background:red;
opacity:.5;
}
See here: http://jsfiddle.net/4yh9L/