I believe it is unnecessary to have "double" navigation as proposed by your designer.
In one of your comments, you said the hierarchy is 3 levels deep, but on the demo site I saw only has 2.
If the navigation is only 2 levels deep
I would just leave it as you have it now. The navigation itself is not very long, so there is not so much content to scroll trough. Making it really easy to understand for users. The navigation is crystal clear this way.
If the navigation is only 3 levels deep
The double navigation might be a good idea for 3 level deep hierarchy, but personally I wouldn't place it into one navigation bar. I consider myself to be tach savvy person, and since I am a designer, I think I understand a lot of different navigational patterns. But I would find this very confusing. I would propose adding additional bar with links to different sections of the document, like in the image below.
- The upside is it is really clear this way. It separates the navigation of the whole website and its main sections, and navigation of the current document.
- The downside here is it takes additional vertical space (which is not so big of an issue nowadays)