Using new order parameters - one proposed by Fredenhagen and Marcu, and another one suggested by ourselves - we have investigated by Monte Carlo method several properties of the transition between the confinement-Higgs phase and the free charge phase of the U(1) lattice Higgs model. These different parameters are constructed by means of gauge invariant 2-point functions and of Wilson loops. The latter show perimeter decay in all phases in the presence of matter fields with unit charge. Nevertheless, appropriate ratios of such 2-point functions and Wilson loops provide sensitive order parameters which are unequal zero in the confinement-Higgs phase but vanish in the free charge phase. We give a heuristic interpretation of this behaviour in terms of dynamical and external charges.