but for the life of me i dont see anywhere where i can INPUT the html to be able to edit it.
Things are a little different at WordPress.com. Here, the Custom Design upgrade gives the option to add or replace CSS to change the appearance of a theme. However, WordPress.com does not give you the option to modify theme HTML. You can move things around using CSS though, and it seems to me that will work just fine for this case.
To move the header image in the Misty Lake theme above the main menu, try adding this to your Appearance → Custom Design → CSS editor:
hgroup {
display: block;
padding-bottom: 120px;
}
.header-image a {
position: absolute;
left: 0;
top: -180px;
}