Reduction from ATM to ATM-complement
By the very same reason you have mentioned there cannot be such a (many-one) reduction. 

Note that if you have two problems, say $A$ and $B$, and $A\le_m B$ then also $\bar A \le_m \bar B$. In fact the same reduction can be used for both statements. So a reduction from ATM to ATM-complement, would also be a reduction from ATM-complement to ATM. And you already know that such a thing does not exist.

If you are however ask for Turing reduction, then the answer is yes. We can ask an ATM oracle and invert the answer to get a Turing machine that decides ATM-complement.