Work-around for missing tab-line-(in)active faces?

Hi,

when I split a window, the mode-line of the inactive window
gets a different style.

I'd like to do that for the tab-line, too, but unlike the
mode-line-(in)active faces there are no such for the tab-line.

With tab-line-tab-name-format-default I can style every single
tab in different ways (and apply whatever face I like), but
I've found no function/hook that allows to apply a different
face to a tab-line itself after e.g. testing if we are in an
inactive window.

Is there any way to style the tab-line with different faces
for active and inactive windows?

Many thanks!

cu,
Frank