If I understand correctly you want a homepage that displays quite differently to your blog page? The content of home and blog can be separate if you go to your dashboard > settings > reading and then set your front page and post page. From reading above it sounds like you might have done this already?
QUICK SOLUTION (Limited, but some options)
1: Two thoughts, you can set your homepage as any page that you've created, and have the content you'd like there. Additionally, you can choose if you'd like the content to display, default (with sidebar) or full width by selecting the page template from the dropdown on the right-hand side when you're editing or creating a page. You could then target the CSS of the page that you set as the homepage and add a background image to the content area. Use / install firebug for firefox if you want to quickly identify which CSS elements / ID's or classes you need to change.
YOU WANT SOMETHING LIKE A MAGAZINE STYLE HOMEPAGE AND THEN A MORE TRADITIONAL BLOG PAGE (Warning PHP skills required and css)
2: Before you proceed I would read this on why you should develop your website as a child theme: http://themeshaper.com/thematic/guide/?page_id=66 If this scenario is what you want you will need some php coding knowledge. There's a free sample child theme that comes with the Themeshaper download, take a look inside the file and find the file called "thematicsamplechildtheme".
If you're already using a child theme then you can skip that link above! For a magazine style homepage (think New York Times style, etc) you would then need to create a home.php file and use a loop to display anything that you wanted. Often people copy the native Themeshaper "index.php" file and then adjust to their display needs through a custom loop and then save that adjusted file as "home.php". Explaining custom loops and homepages is beyond the scope of a simple forum answer but if you can let us all know what you're wanting to do exactly, eg Homepage shows no content but just a background image and then a separate page is a more traditional blog, we can let you know what you might need to consider.
I hope the above helps Zella.