iTerm2 Background image and split panes

This is a year late but I had the same question and ended up here.

There is no way to set a single background for the whole window but if you untick Use Lion-style Fullscreen Windows in the General Preferences, then you can set your background semi-transparent and have your wallpaper act as a single background when iTerm2 is in full screen.

In my case this achieved the result I was looking for in the first place and is an alternative to what you were asking for.

Here's what mine looks like now:

You could also set transparency to 100%.

Note: You may also want to tick Auto-hide menu bar in non-Lion fullscreen in the Appearance tab.

Since iTerm version 3.3.0 (in Beta as of June 2019) you have a setting for this:

In Preferences > Appearance > Panes un-tick Separate background images per pane