This seems to be the best idea for people on a tight gym schedule. The greatest strain on your muscles will come from heavy lifting, so you want to do that first while you still have muscle strength, but your glycogen stores, needed for cardio training, won't have been depleted by your lifts.
Consider cardio secondary. For a well-rounded, fat-busting workout routine, your best bet is to swap the treadmill for resistance training. Strength training moves .
If you cannot then do your cardio after your workouts at least. You also have to do cardio after weights if you have 4-5 cardio sessions and are a serious weight .