  We prove a big monodromy result for a smooth family of complex algebraic
surfaces of general type, with invariants p_g=q=1 and K^2=3, that has been
introduced by Catanese and Ciliberto. This is accomplished via a careful study
of degenerations. As corollaries, when a surface in this family is defined over
a finitely generated extension of Q, we verify the semisimplicity and Tate
conjectures for the Galois representation on the middle \ell-adic cohomology of
the surface.
