The sheet u r talking about is probably being used in a capacitor, but the basic problem lies in the distribution of the charges on the sheet.
Let's assume that we have a cylindrical Gaussian surface(axis perpendicular to the sheet). The length of this cylinder is less than the thickness of the sheet, the electric flux will pass through the 2 bases(considering that half of the cylinder is inside and other half is outside the sheet)
Now flux= closed integral of E.ds
Flux total=2* electric field* area of base
Further E=q/2A£(note distance from the sheet doesn't matter)
Even if combinations of these sheets are taken the NET electric field should always be 0(The distance between sheets doesn't matter)
If only one sheet is taken into account then both the faces have same charge density and field can easily be seen as0
If more than1 sheet is considered the net field inside results in 0