Contrary; the opposite of what's on the surface — used when something runs counter to expectations or appearances.
彼の言葉は親切だが、行動は言っていることと裏腹だ。
His words are kind, but his actions are contrary to what he says.
期待とは裏腹に、売上は伸びなかった。
Contrary to expectations, sales did not increase.
表向きの説明と裏腹に、多くの問題が隠されていた。
Contrary to the official explanation, many problems were hidden.
Indicates that front and back (or two sides) are adjacent or inseparable — an older/slightly formal usage meaning two aspects are directly related or paired.
表と裏は裏腹の関係にあり、一方だけを変えることは難しい。
The front and back are interrelated, and changing only one side is difficult.
このコインは表と裏が裏腹に異なるデザインだ。
This coin has different designs on the two sides that are contrasting.
制度の表向きの利点と裏腹になって被害を受ける人がいる。
There are people who are harmed contrary to the apparent benefits of the system.