Electric field in a quasi-two-dimensional, nanosecond pulse, dielectric barrier discharge in atmospheric air is measured by picosecond four-wave mixing. The results demonstrate electric field offset on the discharge center plane before the discharge pulse, due to surface charge accumulation on the dielectric from the previous pulse. The electric field follows the applied voltage until “forward” breakdown occurs, after which the field in the plasma decreases due to charge separation. When the applied voltage is reduced, the field in the plasma reverses direction and increases again, until the “reverse” breakdown occurs, producing a secondary reduction in the electric field. After the discharge pulse, the field decays on a microsecond time scale. Spatially resolved measurements show that the discharge develops as a surface ionization wave. Significant surface charge accumulation on the dielectric surface is detected near the end of the discharge pulse. Measurements of electric field vector components demonstrate that the vertical field peaks ahead of the ionization wave, while the horizontal field peaks near the ionization wave front. Behind the wave, the vertical field remains low, near the detection limit, while the horizontal field is gradually reduced to near the detection limit at the discharge center plane.