And H1 is a STRUCTURAL tag, a and the heaviest one at that. Do NOT use it in a navigation list. Remember, your navigation items are LIST of links not page headings.
A like the white space in your design. don't be afraid to be elegant and minimalistic. Really the only flaw ( to it's a biggie) is that one CANT tell is the gray box is a sub nav of something.
you really have 3 choices:
1) make it a drop down that flows from its parent.
2) maybe have a b/g graphic like an arrow, that points to the parent
3) make it an 'L ' shape.. that is the links are horizontal, as you have the left edge lined up and it is directly below the parent.
Familiarity is important when it comes to nav and UX.
hope that helps