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Originally Posted by JohnOwens
That was the Cassini/Huygens probe illustrated in rc2000's link above. It was actually Venus-Venus-Earth. But it doesn't really answer the actual question, since OP was asking why not Mars, since it's between us and the outer reaches?
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Timing. Mars just isn't in the right place to be used for gravity assist very often. If it were, I can't think of a reason to not use it. But there are more times when Venus is in a good position. Also, Venus-Venus-Earth gains you a LOT more delta-v than just going by Mars. I'd say probably 5x more.
The problem is not whether one orbit is between two others, but where the planet is in the orbit when you want to try to get elsewhere. Such timings happen a lot less often than one might think. At least, for the things we are trying to do now.