In this paper, it is shown that
Z
2
Z
4
\mathbb {Z}_2\mathbb {Z}_4
-additive codes with additional structure can be viewed as linear codes over rings. As an example, codes over the finite chain ring of order 8,
R
=
Z
4
[
x
]
⟨
x
2
−
2
,
2
x
⟩
R=\frac {\mathbb {Z}_4[x]}{\langle x^2-2,2x\rangle }
, which as additive group is isomorphic to
Z
2
×
Z
4
\mathbb {Z}_2\times \mathbb {Z}_4
, are shown to be
Z
2
Z
4
\mathbb {Z}_2\mathbb {Z}_4
-additive codes. Amongst other results connecting linear codes over
R
R
and their
Z
2
Z
4
\mathbb {Z}_2\mathbb {Z}_4
-additive images, it is shown that the
Z
2
Z
4
\mathbb {Z}_2\mathbb {Z}_4
-additive image of a cyclic code over
R
R
is separable, that is, a direct sum of a binary linear code and a linear code over
Z
4
\mathbb {Z}_4
. The family of chain rings,
Z
4
[
x
]
⟨
x
s
−
2
,
2
x
t
⟩
{\mathbb {Z}_4[x]\over \langle x^s-2, 2x^t\rangle }
, where
1
≤
t
>
s
1\leq t>s
, and the finite commutative local Frobenius non-chain ring
Z
4
[
x
,
y
]
⟨
x
2
−
2
,
x
y
−
2
,
y
2
,
2
x
,
2
y
⟩
\frac {\mathbb {Z}_4[x,y]}{\langle x^2-2,xy-2,y^2,2x,2y\rangle }
are also considered as alphabets for the study of
Z
2
Z
4
\mathbb {Z}_2\mathbb {Z}_4
-additive codes.