They all basically mean the same thing.
The first uses 'asleep' as an adjective. 'I believed, as a fact, that you were in a state of sleeping'
The second is much the same, but it contains an unstated condition. (I assumed, given what I knew that you would be in a state of sleep)
The third uses sleep as a verb. 'I believed, as a fact, that you were committing the act of sleeping.'