front and back; inside and outside; both sides
Refers to the two physical sides of something, such as paper, cloth, a card, or an object with a front and back.
紙の裏表を確認してから印刷してください。
Please check the front and back of the paper before printing.
It is hard to tell the front from the back of this fabric.
inside out; wrong side out
Used especially for clothing or fabric when the inside and outside are reversed; often appears as 裏表に着る or 裏表だ.
I was wearing my T-shirt inside out.
That sock is inside out.
two-facedness; double-dealing; duplicity
Figurative use for a difference between how someone acts outwardly and what they really think or do. Common in patterns like 裏表がある and 裏表のない人.
See also: 表裏
He has no two-facedness in his character and treats everyone the same.
People say that person is a little two-faced.
public face and hidden reality; outward appearance and actual condition; inner workings
Refers to both the visible, official side of something and the less visible reality behind it; often used when someone knows the ins and outs of a world or organization.
He knows the public face and inner workings of this industry thoroughly.
Through years of reporting, she has seen both the outward face and the hidden realities of the political world.
I check which side is front and back before putting on my socks.
I accidentally wore my shirt inside out.
He's a two-faced person, so I can't trust him.
He knows all the ins and outs of the industry.
She's a straightforward person and is liked by everyone.
裏表 refers to the front and back sides of something (or a person's two-facedness), while 裏腹 specifically describes a contrast between outward show and inner truth, and is almost always used with と裏腹に.