The resonance two-photon interaction of the broadband squeezed vacuum with the dipole-forbidden two-level atoms via nonresonant virtual levels is investigated. It is demonstrated that the broadband squeezed vacuum excites coherently the system of radiators (atoms, molecules) that have dipole-forbidden transitions. The quantum statistics of the generated photon pairs in the process of resonance fluorescence is analyzed. As the broadband squeezed field is amplitude-squared squeezed the interaction of this field with the dipole-forbidden atoms can contribute in further amplitude-squared squeezing. In the high-field limit this squeezing increases when the atom number also increases.