Generally, it's considered a bad practice to style standard form controls because the output looks so different on each browser. See: http://www.456bereastreet.com/lab/styling-form-controls-revisited/select-single/ for some rendered examples.
That being said, I've had some luck making the background color an RGBA value:
<!DOCTYPE html>
<html>
  <head>
    <style>
      body {
        background: #d00;
      }
      select {
        background: rgba(255,255,255,0.1) url('http://www.google.com/images/srpr/nav_logo6g.png') repeat-x 0 0; 
        padding:4px; 
        line-height: 21px;
        border: 1px solid #fff;
      }
    </style>
  </head>
  <body>
    <select>
      <option>Foo</option>
      <option>Bar</option>      
      <option>Something longer</option>     
  </body>
</html>
Google Chrome still renders a gradient on top of the background image in the color that you pass to rgba(r,g,b,0.1) but choosing a color that compliments your image and making the alpha 0.1 reduces the effect of this.