  We consider the full set of master integrals with internal top-and
$W$-propagators contributing to the three-loop Higgs self-energy diagrams of
order ${\mathcal O}(\alpha^2 \alpha_s)$. We split the master integrals into a
system relevant to the Feynman diagrams proportional to the product of Yukawa
couplings $y_b y_t$ and the complement. For both systems we define master
integrals of uniform weight, such that the associated differential equation is
in $\varepsilon$-factorised form. The occurring square roots are rationalised
and all master integrals are expressible in multiple polylogarithms.
