In the 2.5D areas, can you move to the front and back instead of only to the left and right?
In double dragon, and in most arcade style games for NES (ninja turtles comes to mind), in the 2.5 d areas you can move front to back and side to side. There is a draw order here too - you will be drawn in front if you are closer - no surprise there really. These "2.5d" areas are part of what made these games so fun, especially for multiplayer.
To handle this movement I would just keep track of the sprites ground position and for the 2d parts of the map only allow x movement and for the 2.5 d parts of the map allow x and y movement and restrict your y range to the ground platform width. Then use your players and enemies ground position y coord to tell which should be drawn first.
As mentioned earlier, when something jumps you can predict where they should land at any given point in time and use that ground position y coordinate to do the depth sorting of sprites.