Actually, JI had 5 A320's at one point, from Fall of 1995 until Spring of 1996. The planes were too big to be profitable on the East Coast routes. So all, but one were disposed of. The remaining A320 was kept until the end of 1998 or thereabouts.
There is no corporate connection between the current Midway and the original, which folded in Fall of 1991, after a proposed sale to Northwest fell through. The only thing in common is the name.
It should also be pointed out that the reason Midway chose the "Midway" name again was that when they were launched, back in Fall of 1993, they did have aspirations to sort of 'revive' the original airline. And todays Midway was indeed originally based out of Midway Airport (MDW). Initially, the routes included DEN, DFW, PHL, DCA, LGA, and BOS.
The move to the current home of RDU took place in Fall of 1995, after heavy losses and lack of available gates at MDW.