The base of the solar convection zone is a region of transition not just for the temperature gradient, but also for the internal rotation of the Sun. The discontinuity in the derivatives of the sound speed at the base of the overshoot layer below the solar convection zone (CZ) introduces a characteristic oscillatory component in the frequencies of solar p modes as a function of the radial order n. The amplitude of this signal can be calibrated using a sequence of solar models constructed with varying extent of overshoot below the CZ base. Using observed solar oscillation frequencies, we find an improved upper limit of 0.05H_p on the extent of overshoot. This technique also allows us to probe the composition profile at the CZ base, and we find that solar models with a sharp change in the composition gradients at the base of the CZ are ruled out from this study. It thus appears that there is some turbulent mixing just below the base of the CZ. The base of the CZ is also the region where the solar rotation rate changes from differential rotation in the CZ to nearly solid-body rotation in the radiative interior. Using modes that have their lower turning points near the transition region, we show that this transition occurs below the CZ base at a radial distance of 0.7050+/-0.0027Rsolar over a half width of 0.0098+/-0.0026Rsolar. We also find an upper limit of 0.3 MG on the toroidal magnetic field concentrated below the CZ base.