Does right-clicking on the window title and selecting "Keep below others" from the dropdown menu solves your problem? I do not have access to a Unity environment at the moment, but as I remember the option always was there.

UPDATE: Ok, after some checking I've found that the option is present in KDE, XFCE and LXDE (Kubuntu, Xubuntu and Lubuntu, respectively), but is disabled/hidden in Gnome, even in older versions.

Also, it seems that GTK does have the required functionality, so it's just a matter of Gnome developers' preference not to expose "unnecessary" or rarely-used settings ("settings kill kittens", as they say). There may or may not be a hidden key somewhere which enables the menu item.

UPDATE 2: I was going to propose you to write a small program which finds a window using, say, gtk_get_window_at_pointer API call and sets it as "always on bottom" with gdk_window_set_keep_below API call (in case you don't mind some programming), but it appears everything has been written for us already: there's a program called Devil's Pie (and also GDevilsPie) which are available in Ubuntu repositories. The program allows you to write some rules which match open windows and perform some actions on them (move to a specific workspace, maximize, minimize etc.)

Here's the documentation

Here's an aricle discussing specifically how to implement "below others" functionality using Devil's Pie or another program called wmctrl

To prevent link rot:

As an example, the first snippet below will toggle the full screen
state of whichever window is selected with the mouse. The second
example does almost exactly what we want, it toggles the always on
bottom state of the active window.

wmctrl -r :SELECT: -b toggle,fullscreen



wmctrl -r :ACTIVE: -b toggle,below