We present new optical emission-line and continuum images taken with HST of the shocked bubble HH 168 (GGD 37) associated with the massive star formation region Cepheus A. The new images clearly resolve the interface between the molecular flow, defined by near-IR images of H_2, and the shocked optically emitting gas. The H_2 emits in a clumpy sheath that surrounds the optical emission in what appears to be a precursor or a C-shock. This region also emits in [S II]. Hence, unlike most other HH regions where [S II] radiates only behind H-alpha in a cooling zone, in HH 168 the [S II] emission leads H-alpha when H_2 emission is present. The [S II] in the precursor/C-shock separates spatially from the H_2; hence, this region is not isothermal. H_2 emission is absent and [O III] is bright near the apices of the high-excitation bow shocks in the flow, as expected from theory.
Radial velocities of H_2 derived from high spectral resolution slit maps of the two highest-excitation HH objects lie within ~ 30 km/s of the molecular cloud velocity, consistent with the precursor scenario. Some of the H_2 emission in the region is redshifted and apparently unrelated to the HH 168 bubble. Additional discoveries include numerous bright point-like H-alpha emission objects, some of which may be T Tauri stars, a bright jet unrelated to the bubble flow, a bumpy morphology to the bright bow shock S, and several locations where `fingers' of H_2 terminate in optically visible HH emission, similar to what is seen in the Orion Nebula.