We present continuum and H alpha imaging polarimetry of the Herbig-Haro objects HH1 and HH2, the faint nebulosity which surrounds them, and nearby stars. We also discuss IRAS observations of the area. We find evidence for a strongly dichroic interstellar medium throughout this region, which polarizes local Hot emission and severely distorts the underlying polarization pattern arising in light scattered from the central object VLA1. It also polarizes nearby stars. This dichroism can be explained by alignment of dust in a magnetic field which, on large scales, is aligned at PA = 126 degrees but, on smaller scales, is distorted within the HH1-HH2 system. Its geometry appears consistent with models of star formation in which a large-scale rotating disc drives an outflow via twisted axial field lines. Both HH1 and HH2 are also associated with small-scale polarization patterns. These can best be understood as resulting from internal dichroic extinction arising in a concentration of well-aligned dust grains lying within the shocked H alpha-emitting regions of these objects. The polarization of HH1 exhibits spiral structure, which may offer support to magnetized jet models, but the polarization of HH2 is more disordered. Our results suggest that further emission-line polarimetry may offer new insights into the structure of HH objects.