The sentence is usually:
"He is in bed sleeping." - he is lying between the sheets, usually with no street clothes on - the usual 'going to bed at night'.
"He is on the bed sleeping." - he is lying on top of the bed-covers (though he may have a rug or blanket over him. He may still be fully clothed except for his shoes.
If you say, "He is sleeping on the bed" (changing the order of the words), you are emphasizing that it is the 'bed' and not the couch or settee or some other alternative.