We present near-infrared [Fe ii] images of four Class 0/I jets (HH 1/2, HH 34, HH 111, HH 46/47) observed with the Hubble Space Telescope (HST) Wide Field Camera 3. The unprecedented angular resolution allows us to measure proper motions, jet widths and trajectories, and extinction along the jets. In all cases, we detect the counterjet, which was barely visible or invisible at shorter wavelengths. We measure tangential velocities of a few hundred kilometers per second, consistent with previous HST measurements over 10 years ago. We measure the jet width as close as a few tens of au from the star, revealing high collimations of about 2° for HH 1, HH 34, and HH 111 and about 8° for HH 46, all of which are preserved up to large distances. For HH 34, we find evidence of a larger initial opening angle of about 7°. Measurement of knot positions reveals deviations in trajectory of both the jet and counterjet of all sources. Analysis of asymmetries in the inner knot positions for HH 111 suggests the presence of a low mass stellar companion at separation 20–30 au. Finally, we find extinction values of 15–20 mag near the source, which gradually decrease moving downstream along the jet. These observations have allowed us to study the counterjet at unprecedentedly high angular resolution and will be a valuable reference for planning future JWST mid-infrared observations that will peer even closer into the jet engine.