I am trying to show the home screen or springboard in the background of launch image.
But what I actually get is in iOS 7
and in iOS 6.1
Is there any possibility of showing home screen or springboard in background while launching the app?
You can't do it. And any home screen screenshot you bundle with your app is never going to match a users actual home screen. As you've seen iOS covers the home screen when an app is launched even if you don't provide a launch image, and if you provide an incorrectly shaped one your app will be rejected at submission.
Just make a launch image as recommended by apple, with a minimal version of your interface on it. It's not a "splash screen" or an opportunity to shove your logo in the users face.