I had to take these steps to support displaying italics in a tmux session. It is documented behavior that screen-* terms do not support italics.

Step 1: Create the following files somewhere on your system

tmux-256color.terminfo.txt

tmux-256color|tmux with 256 colors,
  sitm=\E[3m, ritm=\E[23m,
  smso=\E[7m, rmso=\E[27m,
  use=screen-256color,

tmux.terminfo.txt

tmux|tmux terminal multiplexer,
  sitm=\E[3m, ritm=\E[23m,
  smso=\E[7m, rmso=\E[27m,
  use=screen,

Step 2: Run the following commands to install them to ~/.terminfo/some-number/

tic -o ~/.terminfo tmux-256color.terminfo.txt
tic -o ~/.terminfo tmux.terminfo.txt

Step 3: Set the default terminal for client and server in your .tmux.conf.

set-option -g default-terminal "tmux-256color"
set-option -s default-terminal "tmux-256color"