They are both natural. However the meanings are slightly different. The first means he is still in the hospital, while the second means he was in hospital, but is now out. Also, 'the' isn't strictly necessary. I think it is more natural to just say 'he's in hospital'. I assume in this case that you mean he has been in hospital as a patient? If you were talking about, say, a doctor, who works between his office, a laboratory and a hospital, and someone asked where he was, THEN you would say 'he's in the hospital' (as opposed to some other location). I hope that is helpful, and not too confusing!

They are both natural. Different meanings, of course (as the others have said). I'd say, "He's in hospital" without the 'the' most of the time. He's in hospital. General statement. I don't care which hospital. Same with, "He's in jail/prison." Maybe those things are more of a 'state of being' than a place??? He's in heaven. He's in misery. He's in prison (imprisoned). He's in hospital (sick). Just a thought! I'd add the 'the' if, for some reason, I wanted to be a little more specific (as Hilary says). Perhaps there is only ONE hospital in town, so it'd be 'shared knowledge' - the hospital we both know about. Or I want to differentiate between the clinic, the hospital, and the nursing home. Perhaps.

They are both natural but have different meanings. As to Hilary’s point, in the US, it is necessary to use ‘the’. While many Britishisms are known here, that isn’t one of them.