I suppose Catherine's best known scene in A Mighty Wind was "Mitch and Mickey" singing "A Kiss at the End of the Rainbow":
https://www.youtube.com/watch?v=3eflj2EWZzg

And here's "When You're Next to Me" https://www.youtube.com/watch?v=FMbeMmYkAXQ

The act is vaguely reminiscent of Ian & Sylvia.