  In this paper, we study a relative two-weight $\mathbb{Z}_2
\mathbb{Z}_4$-additive codes. It is shown that the Gray image of a two-distance
$\mathbb{Z}_2 \mathbb{Z}_4$-additive code is a binary two-distance code and
that the Gray image of a relative two-weight $\mathbb{Z}_2
\mathbb{Z}_4$-additive code, with nontrivial binary part, is a linear binary
relative two-weight code. The structure of relative two-weight $\mathbb{Z}_2
\mathbb{Z}_4$-additive codes are described. Finally, we discussed permutation
automorphism group of a $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes.
