I know asleep and sleeping are interchangeable in many cases. But in these situations, I am not sure.
I read stories to my son after he went to bed. After reading the stories, I stayed for some time and tucked the quilt for him. When I came out of his room and met my wife, she asked "Is he asleep?" or "Has he fallen asleep?", or "Is he sleeping?"
In the morning, I woke my son up before he went to school. But later I found he did not get up. His eyes were closed. I asked, "Are you still asleep?" or "Are you still sleeping?"
Which is better in each situation?
asleepto mean actually unconscious. The wordsleepingis sometimes used to refer to being in bed and going to sleep without concern for whether the person has actually fallen asleep yet. So if somebody called for someone, and I knew they were in bed, I'd be much more likely to say "they're sleeping" than "they're asleep". – David Schwartz Apr 22 '12 at 22:51