each time the home page is hit is nothing to do with Front Page configuration - it's the counter itself. It doesn't know which url you come from, it only knows it's been triggered again, so off it goes and adds another hit.
As you have your own domain you are presumably being professionally hosted, and you'll probably find that your hosting company can enable web stats for your site. All good hosts will have this software running on the server, and often it's simply a question of asking them to enable it for you. Once that's done you can access a very detailed log of all site traffic, and you'll be able to see a tally of unique visitors (which is what you're really after, judging by your question). You'll also see which pages got the most attention, which browser your visitors were using, and even which geographical location they came from when they hit your site.