As long as the obstacle is only one square thick, you can throw through it. Stand next to it and lift a character, then extend your throw through the obstacle. Retract your throw range (toward the thrower) and press X at the same time. There is a "sweet spot" to do it right, but because there is no penalty to missing it (you just get an error sound) you can keep extending and retracting while mashing X until you throw straight through the obstacle.