We study the phase diagram of a Z(2) Higgs-gauge model with two specie
s of Ising matter in D = 2 and D = 3. Differently from the case with o
nly one Ising species, this model exhibits a transition also at zero g
auge coupling. Loop expansions and mappings on the 8-vertex and the As
hkin-Teller models are used to study the nature of the transitions in
the extreme regions of the phase diagram. Relevant differences with re
spect to the case of one species of Ising spins are found.