  We analyze a two-field inflationary model consisting of the Ricci scalar
squared ($R^2$) term and the standard Higgs field non-minimally coupled to
gravity in addition to the Einstein $R$ term. Detailed analysis of the power
spectrum of this model with mass hierarchy is presented, and we find that one
can describe this model as an effective single-field model in the slow-roll
regime with a modified sound speed. The scalar spectral index predicted by this
model coincides with those given by the $R^2$ inflation and the Higgs inflation
implying that there is a close relation between this model and the $R^2$
inflation already in the original (Jordan) frame. For a typical value of the
self-coupling of the standard Higgs field at the high energy scale of
inflation, the role of the Higgs field in parameter space involved is to modify
the scalaron mass, so that the original mass parameter in the $R^2$ inflation
can deviate from its standard value when non-minimal coupling between the Ricci
scalar and the Higgs field is large enough.
