We consider a $C^1$-open class of step one skew products of homeomorphisms defined in an interval. The class appeared in previous works of Diaz and Rocha (as a result of a bifurcation), it can also be obtained by perturbation of another class of systems, studied by Alseda and Misiurewicz and by Fan, Simon, and Toth. I will present some results on the structure of the simplex of invariant measures, as well as some results on approximation of ergodic measures with periodic orbits or with horseshoes. This is a joint work with Lorenzo Diaz and Katrin Gelfert.