is it the same to put "I can see he is jumping on his bed" and "I can see him jumping on his bed"? I need to use the first one in a picture description. Can I use it? Would that not sound strange to an native speaker? Thanks in advance.
It can potentially mean the same. Though "I can see him jumping on his bed" can also be interpreted as "I imagine him jumping on his bed." Admittedly, this is a strange interpretation of the sentence and probably not true, but you should be aware of this second meaning.
Used in another context:
"I can see him laying on the beach with shades on."
In this interpretation, the speaker doesn't literally mean the person is within sight on the beach. It means it imagines him laying on the beach with shades on.