When using the “Cut Through” function from the Edit menu, a dialogue box opens to allow the Overlap to be specified. Instead of an overlap, a void is created between the two halves of the object that has been “Cut Through”. This void, when measured, is the same dimensions as the overlap requested.
In case you want to add an overlap to both objects you need to use the Pagination tool instead of the cut through feature. The Pagination tool is also available under the Edit Menu.