That's how the tabbed docks work and as far as I know there's no way to hide the tabs themselves. Some of the tab themes are pretty transparent, for example "Bubble", if it's purely a cosmetic issue. And of course you could use text and theme coloration to blend the tabs into your wallpaper. But I don't think you can actually put them into a hidden state.
You could go with an autohiding untabbed dock, but I'm guessing you already know that and prefer a tabbed dock. (Don't forget that you can have multiple untabbed docks loaded at the same time, or untabbed docks loaded while tabbed docks are also loaded.)
