  We study a model of multiple-field DBI inflation leading to mixed form of
primordial non-Gaussianity, including equilateral and local bispectrum shapes.
We present a general formalism based on the Hamilton-Jacobi approach, allowing
us to go beyond slow-roll, combining the three-point function for the fields at
Hubble-exit with the non-linear evolution of super-Hubble scales. We are able
to obtain analytic results by taking a separable Ansatz for the Hubble rate. We
find general expressions for both the equilateral and local type
non-Gaussianity parameter fNL. The equilateral non-Gaussianity includes the
usual enhancement for small sound speeds, but multiplied by an analytic factor
which can lead to a suppression. We illustrate our results with two scenarios.
In the first model, previously found to have detectable local non-Gaussianity,
we find that the equilateral signal is not sufficiently suppressed to evade
current observational bounds. In our second scenario we construct a model which
exhibits both a detectable equilateral fNL and a negative local fNL.
