In how many ways can a President, Vice-President, and Treasurer be chosen from a group of $4$ guys and $4$ girls and at least one girl and at least one guy holds at least one of those three positions? One person cannot serve in more than one position.
We have $8$ choices for president, $7$ choices for vice-president, and $6$ choices for treasurer, for a total of $8\times7\times6 = 336$ choices. Now we have to subtract the number of choices that don't satisfy the requirement, where the $3$ officers are all boys or all girls. For either case, we have $4$ choices for president, $3$ choices of vice-president, and $2$ choices for treasurer, a total of $4\times3\times2 = 24$ choices. So we have $2\times 24 = 48$ total choices that don't satisfy the requirement.

Thus, there are $336-48=\boxed{288}$ good choices.