Astronomy and Astrophysics 552 (2013): A4 reproduced with permission from Astronomy and Astrophysics ; Context. Circumstellar disks are believed to be the birthplace of planets and are expected to dissipate on a timescale of a few Myr. The processes responsible for the removal of the dust and gas will strongly modify the radial distribution of the circumstellar matter and consequently the spectral energy distribution. In particular, a young planet will open a gap, resulting in an inner disk dominating the near-IR emission and an outer disk emitting mostly in the far-infrared. Aims. We analyze a full set of data involving new near-infrared data obtained with the 4-telescope combiner (VLTI/PIONIER), new mid-infrared interferometric VLTI/MIDI data, literature photometric and archival data from VLT/NaCo/SAM to constrain the structure of the transition disk around T Cha. Methods. After a preliminary analysis with a simple geometric model, we used the MCFOST radiative transfer code to simultaneously model the SED and the interferometric observables from raytraced images in the H-, L′-, and N-bands. Results. We find that the dust responsible for the strong emission in excess in the near-IR must have a narrow temperature distribution with a maximum close to the silicate sublimation temperature. This translates into a narrow inner dusty disk (0.07-0.11 AU), with a significant height (H/r ∼ 0.2) to increase the geometric surface illuminated by the central star. We find that the outer disk starts at about 12 AU and is partially resolved by the PIONIER, SAM, and MIDI instruments. We discuss the possibility of a self-shadowed inner disk, which can extend to distances of several AU. Finally, we show that the SAM closure phases, interpreted as the signature of a candidate companion, may actually trace the asymmetry generated by forward scattering by dust grains in the upper layers of the outer disk. These observations help constrain the inclination and position angle of the disk to about + 58 and - 70, respectively. Conclusions. The circumstellar environment of T Cha appears to be best described by two disks spatially separated by a large gap. The presence of matter (dust or gas) inside the gap is, however, difficult to assess with present-day observations. Our model suggests the outer disk contaminates the interferometric signature of any potential companion that could be responsible for the gap opening, and such a companion still has to be unambiguously detected. We stress the difficulty to observe point sources in bright massive disks, and the consequent need to account for disk asymmetries (e.g. anisotropic scattering) in model-dependent search for companions