Michael thought the same as I did,he thought that you are away on holiday.

[Jit833]

1) Michael was under the wrong belief/impression that you were on holiday just like I had.
2) Michael thought the same as I did,he thought that you are away on holiday.

 

[Raymott]

1) Michael was under the [STRIKE]wrong[/STRIKE] mistaken belief/impression that you were on holiday, just as I was. [STRIKE]like I had[/STRIKE]. This is ambiguous. Can you tell why?
2) Michael thought the same as I did - that you were away on holiday.

For 1. you can't say "Michael was ... just like I had".
2. That's just one possible solution.