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If you cut the box in 2, to create the main body and lid, then a 3/8" rabbet around the outside of the main body and a 3/8" rabbet around the inside of the lid, the lid will slip down by the 3/8" inch. So you thinking is correct, add an additional 3/8" to the overall height of the sides.

come to think of it, you might want to add for the kerf of the blade your going to use to cut the box in 2....
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