The frequency distributions of hydrogen lines broadened by the local fields of both ions and electrons in a plasma are calculated in the classical path approximation. The electron collisions are treated by an impact theory which takes into account the Stark splitting caused by the quasi-static ion fields. The ion field-strength distribution function used includes the effect of electron shielding and ion-ion correlations. The various approximations that were employed are examined for self-consistency and an accuracy of about 10% in the resulting line profiles is expected. Good agreement with experimental ${\mathrm{H}}_{\ensuremath{\beta}}$ profiles is obtained while there are deviations of factors of two with the usual Holtsmark theory. Asymptotic distributions for the line wings are given for astrophysical applications. Also here the electron effects are generally as important as the ion effects for all values of the electron density and in some cases the electron broadening is larger than the ion broadening.