We compute the tunneling probability from the symmetric phase to the true vacuum, in the first-order electroweak phase transition of the MSSM, and the corresponding Higgs profiles along the bubble wall. We use the resummed two-loop temperature-dependent effective potential, and pay particular attention to the light stop scenario, where the phase transition can be sufficiently strongly first-order not to wipe off any previously generated baryon asymmetry. We compute the bubble parameters which are relevant for the baryogenesis mechanism: the wall thickness and Δβ. The two-loop corrections provide important enhancement effects, with respect to the one-loop results, in the amount of baryon asymmetry.