Context. The young stellar object (YSO) Th 28 possesses a highly collimated jet, which clearly exhibits an asymmetric brightness of its jet lobes at optical and near-infrared wavelengths. As with many other YSO outflows, there may be asymmetry in the physical parameters of the jet plasma in opposite jet lobes (e.g. electron density, temperature, and outflow velocity). Aims. We examined the Th 28 jet at high-spatial resolution in the regions where the jet material is collimated and accelerated. Our goal is to map the morphology and determine its physical parameters. We compared the results with those of other asymmetric YSO jets to determine the physical origin of such asymmetries. Methods. We used the integral field spectrograph SINFONI on the Very Large Telescope (VLT) of the European Southern Observatory to characterise the jet parameters in a 3″ × 3″ field around the central source of Th 28. We present high-resolution spectra of Th 28 covering the JHK bands, obtained in June-July 2015. Results. The images reveal gaseous structures out to distances of a few arcseconds around the stellar jet source. The [Fe II] emission originates in highly collimated jet lobes. Two new axial knots are detected in the bipolar jet, one in each lobe, at angular distances of 1″ in the blue lobe and 1″​​.2 in the red lobe. The H₂ radiation is emitted from an extended region with a radius of ≳270 au, which is perpendicular to the jet. The position–velocity diagrams of the bright H₂ lines reveal faint H₂ emission along both jet lobes as well. The compact and faint H I emission (Paβ and Brγ) comes from two regions, namely from a spherical region around the star and from the jet lobes. The maximum size of the jet launching region is derived as 0″​​.015, which corresponds to ∼3 au at a distance of 185 pc, and the initial opening angle of the Th 28 jet is about 28°, which makes this jet substantially less collimated than most jets from other Classical T Tauri stars (CTTs). Conclusions. The high-resolution SINFONI images show three groups of lines with different excitation conditions, which trace different gas structures. The emission in [Fe II], H₂, and atomic hydrogen lines suggests a morphology in which the ionised gas in the disc (or at least very close to the jet launching site) appears to be disrupted by the jet. The resolved disc-like H₂ emission most likely arises in the disc atmosphere from shocks caused by a radial uncollimated wind. The asymmetry of the [Fe II] photocentre shifts with respect to the jet source arises in the immediate vicinity of the driving source of Th 28 and suggests that the observed brightness asymmetry is intrinsic as well.