We present novel calculations of the magnetic dichroism appearing in molecular bands in the presence of a strong magnetic field, which perturbs the internal structure of the molecule and results in net polarization due to the Paschen-Back effect. Based on that, we analyze new spectropolarimetric observations of the cool magnetic helium-rich white dwarf G99-37, which shows strongly polarized molecular bands in its spectrum. In addition to previously known molecular bands of the C2 Swan and CH A-X systems, we find a firm evidence for the violet CH B-X bands at 390 nm and C2 Deslandres-d'Azambuja bands at 360 nm. Combining the polarimetric observations with our model calculations, we deduce a dipole magnetic field of 7.5+/-0.5 MG with the positive pole pointing towards the Earth. We conclude that the developed technique is an excellent tool for studying magnetic fields on cool magnetic stars.