If you want to use the “index.php” of your theme as the front page, then disable the static home page. Go to Settings -> Reading Settings -> Front page displays and select the “Your latest posts” radio button.
Technically, the “index.php” in the root of your WP install is the home page. Thanks to the wonders of PHP and MySQL, WP just applies your options to dynamically display the home page content of your choice, whether it’s a “static” page or the index.php of your theme, which usually displays the most recent posts.
Does that help? Or is there something else you are trying to do? If so, please be more specific.
If you have template pages in your theme for every other purpose (single.php, archive.php, search.php, page.php, etc.), then the theme’s index.php file is only used as your front blog page. For one site, I have customized mine to be more like a regular website home page instead of a blog.