Is this correct?

Are you asking if "somebody's" should be capitalized? That depends upon whether or not the phrase appears at the beginning of a sentence--if it does, than yes, it should be "Somebody's"--otherwise, no.

As for "interview by" versus "interview with," i'd personally prefer "inteview with."

I tend to agree. "Interview by" would expect a named to follow

e.g.

"My interview by Elmer Fudd of CNN"

thanks!

thank you