The FIR part is first extracted, and the (strictly proper) remainder is passed to residuez for expansion of the IIR part (into a sum of complex resonators). One must remember that, in this case, the impulse-response of the IIR part begins after the impulse-response of the FIR part has finished, i.e.,
See §6.8.8 for an example usage of residued (with a comparison to residuez).
Matlab listing: mps.m
Example with Repeated Poles