When I ask about somebody's occpation.

[wotcha]

For examples, when I ask about the occupation of my friend's, can I say

"What is your father?" or
"Who is your father?"

[emsr2d2]

For examples, when I ask about the occupation of my friend's, can I say

"What is your father?" or
"Who is your father?"

Neither.

What is your father? My father is a man.
Who is your father? My father is Mr Smith.

What does your father do [for a living]? He's a doctor.

[2006]

For example, when I ask about the occupation of my friend's, can I say

"What is your father?" In the right context, this one would work.
My father is a mechanic. What is your father?

But without context, use emsr2d2's last quuestion.
"Who is your father?"

2006

[wotcha]

2006

I see. Thank you very much.