The ratio of the vertical-to-horizontal peak ground accelerations highlights that values greater than one tend to happen in the near-fault area, where the corresponding ratio of spectral accelerations may be amplified in the range of low vibration periods. The high vertical-to-horizontal stiffness of a base-isolation system (e.g. high-damping-rubber bearings, HDRBs) of a reinforced concrete (RC) framed structure causes that the superstructure behaves like fixed-base in the vertical direction. Seismic damage induced by vertical excitation is generally located at the upper storeys, where the effects of gravity loads generally prevail over those of the horizontal loads and an amplification of the vertical motion is expected. In the present work, attention is focused on the combination of horizontal and vertical base-isolation resulting from the in-series vertical arrangement of HDRB and super HDR layer, the latter not affecting the horizontal stiffness of the isolator but reducing its vertical stiffness. The main objective is the evaluation of the isolation ratio in the vertical direction that needs to be considered for an effective protection against significant vertical near-fault earthquakes. A five-storey RC framed structure is first designed as fixed-base in a medium-risk zone, in compliance with a former Italian seismic code (DM96). It is retrofitted by the insertion of a horizontal-vertical base-isolation system, with upper- and lower-bound design properties defined by current European code for antiseismic devices (UNI-EN15129). Nonlinear seismic analysis of the test structures is carried out considering near-fault earthquakes selected from the Pacific Earthquake Engineering Research Center database and scaled to match the design spectrum of acceleration. Finally, the vertical stiffness to be assigned to the isolation system to obtain shifting from the vibration periods of maximum amplification is evaluated by wavelet analysis, including moving resonance effect induced by inelastic deformation of the superstructure.