We analyzed the seismological data collected by the InSight mission, which landed on Mars in November 2018, in order to reveal the first tens of meters of the subsurface structure underneath the landing site. Here, we performed horizontal-to-vertical analysis (H/V) for different wind-dependent noise periods and for martian seismic events data (marsquakes). The final H/V curve presents a characteristic trough at 2.4 Hz and a strong peak at 8 Hz. We inverted this H/V curve for the 1D shear-wave velocity structure at the InSight landing site. Based on our inversion results, we propose a strong site effect at the InSight site to be due to the presence of a shallow high-velocity layer (SHVL) over low-velocity units. The SHVL is likely placed below a layer of coarse blocky ejecta and can be associated with Early Amazonian basaltic lava flows. The units below the SHVL have lower velocities, possibly related to a Late Hesperian or Early Amazonian epoch with a different magmatic regime and/or a greater impact rate and more extensive weathering. An extremely weak buried low-velocity layer (bLVL) between these lava flows explains the data around the 2.4 Hz trough, whereas a more competent bLVL would not generate this latter feature. These subsurface models are in good agreement with results from hammering experiments and compliance measurements at the InSight landing site. Finally, this site effect is revealed only by seismic events data and it explains the larger horizontal than vertical ground motion recorded for some marsquakes.