There's never been a US dime with a building on the back.
Cents, nickels, and half dollars at one time or another have had pictures of various buildings, but if you look at any of the dimes in your pocket you'll see that none of them have a building.
Please see the Related Question for more details.
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The back of a US $10 bill shows the US Treasury Building.
Note that all current American bills have captions on them identifying the person pictured on the front and the scene or building on the back.
Monticello, the home of Thomas Jefferson 3rd president. The name is right under the building in small letters.
There has never been a building depicted on the reverse of a US dime. Please see the Related Question for more.
The White House.
Note that all current US bills have captions identifying the portrait shown on the front and the scene or building on the back.