You can increase the height of the background so it as big as you want your map to be. Then you add a check to your sprite that if its Sprite.Y < Windowheight / 2 for instant, then you move everything down Y by a certain amount otherwise your sprite will jump out of the screen.
So if Sprite.Y < WindowHeight / 2 (Which would mean if the sprite move above the middle of the screen)
Set Sprite.Y = Sprite.Y + <Some value>
Set background.Y = Background.Y + <Same value as above>
It would probably be easiest to just add all the objects that needs to scroll to a family. And just use that instead.