  Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex
numbers. A holomorphic triple $(E_1,E_2,\phi)$ on $X$ consists of two
holomorphic vector bundles $E_{1}$ and $E_{2}$ over $X$ and a holomorphic map
$\phi \colon E_{2} \to E_{1}$.
  There is a concept of stability for triples which depends on a real parameter
$\sigma$.
  In this paper, we determine the Hodge polynomials of the moduli spaces of
$\sigma$-stable triples with $\mathrm{rk}(E_1)=\mathrm{rk}(E_2)=2$, using the
theory of mixed Hodge structures (in the cases that they are smooth and
compact).
  This gives in particular the Poincar{\'e} polynomials of these moduli spaces.
  As a byproduct, we also give the Hodge polynomial of the moduli space of even
degree rank 2 stable vector bundles.
