I do exactly what you want. I use wordpress as a backend for a few regular websites. I found it easiest to design an empty theme. I basically removed everything, so that only raw html displays. It ends up looking like this: http://www.mybeausejour.com/wordpress/
If you look at the html for that, you'll see just about everything has been removed. Customizing a theme this way is easy, as you basically remove almost everything except the loop.
Then I design my regular site, and i use php to getfilecontents from the wordpress site. I use the full uri, with http in it, so it will give a full uri and path to any images inserted. You could actually have the wordpress site under a completely different domain if you like.
Here is how that same content looks on the public face of the site: http://mybeausejour.com
I did it this way as the original site was already there. Rather than go to a lot of work to design a wordpress theme that looks the same, I just simplified the wordpress theme, pulled data from it, and included it where needed on my site.