The only way you're going to be able to do this is by getting fancy with some CSS and javascript. CSS doesn't support blur directly, but you can emulate it with text-shadow. Images can also be blurred with a little jquery/css/javascript magic, but will be problematic because you can't partially blur an image (what happens when only part of the image is under the banner?). It could probably be done by layering your images and keeping track of their position on screen, but all of this seems like a lot of work for a very small return.
So, assuming you've decided to give all of this a shot, you're going to have to use javascript to determine which parts of the page have passed under the banner and apply the style to those parts. The difficulty of this task will scale with the complexity of your page layout. In a best case scenario, your banner and content container are both 100% the width of the html body. At this point, it would be fairly trivial to write some kind of scanner that traverses the dom every time you page scroll to find elements that the blur should be applied to. However, best-case-scenario is rarely the case at hand, at which point I'd recommend abandoning the effort to pursue something with a greater ROI.