Underline instead of italic in org mode

Move point to something that's not displayed as you want, and hit C-u C-x =. This will bring up a new buffer with information about the character at point.

The piece you're interested in is this:

There are text properties here:
  face                 (italic)

(You might have something else than italic there.)

In my Emacs, italic is a link to a page where you can customize the face. You can also type M-x customize-face RET italic directly. In the Customize buffer that appears, you can change what the text should look like.

I had the same problem. Using a fresh installation of emacs would give me underlined text for text inside of // instead of slanted text. While using the customize-face-editor could solve the problem somehow, the solution looked messy inside my init-file and I did not understand it, which I found unpleasant. Therefore I investigated to solve the problem with "set-face-attribute". Here is what worked for me:

(set-face-attribute 'italic nil
                :slant 'italic 
                :underline nil)

Note: set-face-attribute is a function which takes a 'face and can set several :attributes with regard to the face. The "nil" is set to apply the settings to every frame.