  We consider a model of two-field inflation, containing an ordinary scalar
field and a DBI field. We work beyond the slow-roll approximation, but we
assume a separable Hubble parameter. We then derive the form of potential in
this framework and study the spectrum of the primordial perturbations in
details. We also study the amplitude of the non-Gaussianity of the primordial
perturbations both in equilateral and orthogonal configurations in this setup.
We test the model with recent observational data and find some constraints on
the model parameters. Our study shows that for some ranges of the DBI
parameter, the model is consistent with observation and it is also possible to
have large non-Gaussianity which would be observable by future improvements in
experiments.
