Interaction of brushes oriented face-to-face under compression and subsequent extension is investigated theoretically. Brushes formed by mesogenic chains with induced stiffness in the liquid-crystalline (LC) state are considered. It is shown that the contact between LC brushes composed of long folds of grafted chains (FLC structure) leads to interpenetration of brushes and to formation of a combined structure. The brushes remain combined under the extension of this structure.