Eight beams of 0.35 μm laser with pulse duration of 1 ns and total energy of 2 kJ enter into a hohlraum to create intense X-ray radiation of 140 eV on the Shenguang Ⅱ laser facility. Plastic foam (C6H12) and copper-doped foam (C6H12Cu0.394) with a density of 50 mg/cm3 are heated by X-ray radiation emitted from the hohlraum. The breakout time of the radiation wave is measured by a tri-chromatic streaked X-ray spectrometer (TCS) that consists of a set of three imaging pinholes and an array of three transmission gratings coupled with an X-ray streak camera (XSC). At one shot, the simultaneous measurements of the delay of the drive source and the radiation transport at two energies (210 eV, 840 eV) through the foam have been made for the first time. The experimental results indicate that the time delays vary with photon energies. With a transmission grating spectrometer (TGS), the spectra transmitting foams were measured, and the lower limit of the optical depth was measured. The radiation at energy of 210 eV propagates through plastic foam at a faster velocity, compared with the radiation at energy of 840 eV; while the results of copper-doped foam are reverse. The optical depth in the plastic foam is less than 1, and in the doped foam it is more than 1.