  We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that
the partition function is an isomonodromic tau function in a sense that
generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need
to define a notion of tau-function for isomonodromic systems where the
ad-regularity of the leading coefficient is not a necessary requirement.
