Hinode discovered a beautiful giant jet with both cool and hot components at the solar limb on 2007 February 9. Simultaneous observations by the Hinode SOT, XRT, and TRACE 195 satellites revealed that hot (5x10^6 K) and cool (10^4 K) jets were located side by side and that the hot jet preceded the associated cool jet (1-2 minutes). A current-sheet-like structure was seen in optical (Ca IIH), EUV (195A), and soft X-ray emissions, suggesting that magnetic reconnection is occurring in the transition region or upper chromosphere. Alfven waves were also observed with Hinode SOT. These propagated along the jet at velocities of 200 km/s with amplitudes (transverse velocity) of 5-15 km/s and a period of 200 s. We performed two-dimensional MHD simulation of the jets on the basis of the emerging flux-reconnection model, by extending Yokoyama and Shibatas model. We extended the model with a more realistic initial condition (10^6 K corona) and compared our model with multiwavelength observations. The improvement of the coronal temperature and density in the simulation model allowed for the first time the reproduction of the structure and evolution of both the cool and hot jets quantitatively, supporting the magnetic reconnection model. The generation and the propagation of Alfven waves are also reproduced self-consistently in the simulation model.