Okay. First, to basically zero out as much of the current menu styles as possible, what I did was go to Appearance → Custom Design → CSS, click "Edit" next to "Mode: Add-on," click the theme CSS link, and looked for the section named "=Menu Ribbon-style." Then I systematically added CSS rules to override the ones listed there until I came up with this list of stuff to reset:
#navigation,
#navigation > .main-menu:before,
#navigation > .main-menu:after,
#navigation .main-menu > ul:before,
#navigation .main-menu > ul:after {
border: none;
}
#navigation:before,
#navigation:after,
#navigation > .main-menu > ul {
background: none;
box-shadow: none;
}
#navigation > .main-menu {
background-color: inherit;
}
To add the image you provided in as a background for the main navigation, do this:
#navigation {
background: url('http://tacklingmommyhood.files.wordpress.com/2013/01/screen-shot-2013-01-03-at-12-05-58-am.png') 9px 0 no-repeat;
}
I noticed it feels like there's a 1px line above the menu with this solution, but that's actually in the header image itself just below the grass: http://tacklingmommyhood.files.wordpress.com/2012/12/banner-grass-dec-27-2012-poles-stroller-copy1.png