In this paper we emphasize the non-Lorentzian behavior of the Balmer series in helium-dominated DBA white dwarf stars for which the decades-old problem exists for the determination of the hydrogen abundance. In a very recent work, we have shown that quasi-molecular line satellites due to H-He and H-H collisions are responsible for the asymmetrical shape of the Lyman-α lines observed with the Cosmic Origin Spectrograph and that a similar asymmetry exists for the Balmer-α line profiles. In continuation with very recent work, where the n = 2, 3 potential energies and transition dipole moments from the ground state were determined, here, we present accurate H-He potential energies and electronic transition dipole moments concerning the molecular states correlated with H(n = 4)+He and their transition dipole moments with the states correlated with H(n = 2)+He. Those new data are used to provide a theoretical investigation of the collisional effects in the blue wing of the Balmer-β line of H perturbed by He. Because of the general trend characterizing the repulsive Σ states of the potential energies involved in the Balmer series, the amplitude in the core of the line is decreasing very fast with the order of the series when the helium density gets as large as 1021 cm−3. This study is undertaken by applying a unified theory of spectral line broadening that is valid at very high helium densities found in DZA white dwarf stars. The treatment includes collision-induced line satellites due to asymptotically forbidden transitions, and it explains the asymmetry observed in their spectra.