Microdosimetric single event spectra as a function of depth in a phantom for the 290 MeV/nucleon therapeutic carbon beam at HIMAC were measured by using a tissue equivalent proportional counter (TEPC). Two types of geometries were used: one is a fragment particle identification measurement (PID-mode) with time of flight (TOF) method without a backward phantom, and the other is an in-phantom measurement (IPM-mode) with a backward phantom. On the PID-mode geometry, fragments produced by carbon beam in a phantom are identified by the DeltaE-TOF distribution between two scintillation counters positioned up- and down-stream relative to the tissue equivalent proportional counter (TEPC). Lineal energy distributions for carbon and five ion fragments (proton, helium, lithium, beryllium and boron) were obtained in the lineal-energy range of 0.1-1000 keV/microm at eight depths (7.9-147.9 mm) in an acrylic phantom. In the IPM-mode geometry, the total lineal energy distributions measured at eight depths (61.9-322.9 mm) were compared with the distributions in the PID-mode. Both spectra are consistent with each other. This shows that the PID-mode measurement can be discussed as the equivalent of the phantom measurement. The dose distribution of the carbon beam and fragments were obtained separately. In the depth dose curve, the Bragg peak was observed. Relative biological effectiveness (RBE) for the carbon beam in the acrylic phantom was obtained based on a biological response function as a lineal-energy. The RBE of carbon beam had a maximum of 4.5 at the Bragg peak. Downstream of the Bragg peak, the RBE rapidly decreases. The RBE of fragments is dominated by Boron particles around the Bragg peak region.