The geodynamic evolution of the Western Mediterranean for the past 35My is a matter of debate. Present-day structure and composition of the lithosphere and sublithospheric mantle may help in constraining the geodynamic evolution of the region. We use an integrated geophysical-petrological modeling to derive and compare the present-day thermal, density and compositional structure of the lithosphere and sublithospheric mantle along two NNW-SSE oriented geo-transects crossing the back-arc Alboran and Algerian basins, from onshore Iberia to the northern Africa margin. The crust is constrained by seismic experiments and geological cross-sections, whereas seismic tomography models and mantle xenoliths constrain the upper mantle structure and composition. Results show a thick crust (37km and 30km) and a relative deep LAB (130km and 150km) underneath the HP/LT metamorphic units of the Internal Betics and Greater Kabylies, respectively, which contrast with the 16km thick magmatic crust of the Alboran Basin and the 10km thick oceanic crust of the Algerian Basin. The sharp change in lithosphere thickness, from the orogenic wedge to the back-arc basins, contrasts with the gentler lithosphere thickening towards the respective opposed margins. Our results confirm the presence of detached slabs ~400^oC colder than upper mantle and a fertile composition than the continental lithospheric mantle beneath the External Betics and Saharan Atlas. Presence of detached quasi-vertical sublithospheric slabs dipping towards the SSE in the Betics and towards the NNW in the Kabylies and the opposed symmetric lithospheric structure support an opposite dipping subduction and retreat of two adjacent segments of the Jurassic Ligurian-Tethys realm.