Oh wait, I just realized you're creating a side scroller type game, not a top down, which introduces a different set of problems. The objects come out of the background when you jump? Very strange, did you set up your camera with any sort of zoom?
No zoom; the objects render in the background when they're supposed to be between the player and the map (not behind the map), which is visible given the order of the render calls. If the player jumps, the objects move faster on the Y axis than the environment, though it should just be the same, giving it a strange parallax effect. Interestingly, if I create a BitmapFont and try to render some text on the screen, it looks like it's rendered relative to the world and not the screen:
font.draw(batch, "HP: " + player.stats.health, 10, 10);
That call draws that string in the world, so I can walk and see it as if it were written on the background. This is placed within a batch.begin() and batch.end() and the batch is acquired from the renderer. This and the other issue may be related.