  We discuss the geometry of some arithmetic orbifolds locally isometric to a
product of real hyperbolic spaces of dimension two and three, and prove that
certain sequences of non-uniform orbifolds are convergent to this space in a
geometric ("Benjamini--Schramm") sense for hyperbolic three--space and a
product of hyperbolic planes. We also deal with arbitrary sequences of maximal
arithmetic three--dimensional hyperbolic lattices defined over a quadratic or
cubic field. A motivating application is the study of Betti numbers of Bianchi
groups.
