We further develop a form factor formalism characterizing anomalous interactions of the Higgs-like boson ( h) to massive electroweak vector bosons ( V) and generic bilinear fermion states . Employing this approach, we examine the sensitivity of pp → → V h associated production to physics beyond the Standard Model, and compare it to the corresponding sensitivity of h → V decays. We discuss how determining the Vh invariant-mass distribution in associated production at LHC is a key ingredient for model-independent determinations of hV interactions. We also provide a general discussion about the power counting of the form factor's momentum dependence in a generic effective field theory approach, analyzing in particular how effective theories based on a linear and non-linear realization of the SU(2)L × U(1)Y gauge symmetry map into the form factor formalism. We point out how measurements of the differential spectra characterizing h → V decays and pp → → Vh associated production could be the leading indication of the presence of a nonlinear realization of the SU(2)L × U(1)Y gauge symmetry.