We consider mixed strong-electroweak corrections to Higgs production via gluon fusion, in which the Higgs boson couples to the top quark. Using the method of differential equations, we compute all of the master integrals that contribute to this process at two loops through O ( ϵ 2 ) in the dimensional regularization parameter ϵ = ( d − 4 ) / 2 , keeping full analytic dependence on the top quark, Higgs, W , and Z boson masses. We present the results for these master integrals in terms of iterated integrals whose kernels depend on elliptic curves.