The lithosphere-asthenosphere boundary (LAB) is characterized by a sharp reduction in seismic wave speed and increased electrical conductivity. A partial melt layer is classically proposed to explain these geophysical characteristics. However, a main question remains to be answered, e.g. how such a layer can be stable while buoyant melts should rise through the lithosphere. We measured the density and structure of carbonated alkali basalts taken as a proxy for LAB melts in situ at high pressure (P) and temperature (T) conditions. We found them to be neutrally buoyant at the P-T conditions of the LAB under continents, and provide structural insights on melt compaction mechanisms. Neutral buoyancy implies the stability of a partial melt layer at these depths. Basalts generated below the lithosphere may accumulate over time, eventually reaching several % melt. Their presence provide answers to key questions on continental