'He's dead' is correct. It's quite blunt, and some people might not like the use of the word 'dead'. However, I think as the speaker is talking about their own dad, it's perfectly fine. 'He's been dead' is only correct if you add a duration, e.g. 'He's been dead for many years'. 'He passed away' is also correct. It's softer and euphemistic than using 'dead'.

"He passed away" is a lot more polite, but "He's dead" makes sense too.

In Heaven

He passed away.

He passed away./He died. /He has departed. /He is no longer with us.