The electric field change of a femtosecond mid-infrared (MIR) pulse reflected by a new type of Bragg mirror is directly measured by time-resolved cross-correlation spectroscopy. The refractive-index contrast of the plasma Bragg mirror is achieved by use of different doping levels of only one type of semiconductor material (n(+) -doped GaAs and undoped GaAs). The direct measurement of the time dependence of the electric field of a reflected MIR pulse permits the observation of a noninstantaneous response of a Bragg mirror compared with a metallic surface, which is due to the penetration of the pulse into the multilayer structure.