A double discontinuity is a compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer on the postshock side. We use high-resolution data from Geotail and Wind spacecraft to examine the interior structure within the finite thickness of the discontinuity at the plasma sheet-lobe boundary and found that recognizable MHD structures at the boundary can be stand-alone slow shocks or double discontinuities. The plasma density increases significantly and the magnetic field intensity decreases significantly across the interior of the slow shock layer. Through the rotational layer, the magnetic field rotates about the normal direction of the shock surface, as the plasma density and the magnetic field intensity remain nearly unchanged. The rotational angle can vary over a wide range. We notice that the observations of double discontinuities are no less frequent than the observations of stand-alone slow shocks. Identification of slow shocks and double discontinuities infers that plasma and magnetic field lines continuously move across the boundary surface from the lobe into the plasma sheet, and there is a conversion of magnetic field energy into plasma thermal energy through the slow shock layer. The double discontinuities also allows for a rapid rotation of the postshock magnetic field lines immediately behind the shock layer to accommodate the environment of the MHD flow in the plasma sheet region.<br><br><b>Key words. </b>Magnetospheric physics (plasma sheet) Space plasma physics (discontinuities; shock waves)