Maybe this isn’t what you are looking for, but instead of trying to make the div fit the height, just worry about the container div and add a double border to it. You can use something like
border: 4px double #000;
for a double border. Or if you have a border image, you could use the css3 border image.
Here is an example of css only double, triple and quadruple borders. I’m sure you could add more using :before and :after, but I think this should give you an idea. Using the outline and outline-offset, you can make the border a different color, size or style (e.g. dotted).