We study the properties of the broad-line region in blazars by comparing the virial estimate of black hole masses with that derived from the mass of the host galaxies. The former is sensitive to the width of broad lines, i.e. to the projection of the velocity of line-emitting clouds along the line of sight; the latter is not. This comparison allows us to constrain the deprojection factor f, thus revealing general properties of the geometry of the broad-line region. We show that blazars tend to have (1) higher f values than the quasars of our reference sample: 〈f BLLacs〉= 6.9 ± 2.3; 〈f blazars〉= 5.6 ± 1.3 and 〈f quasars〉= 2.0 ± 0.3, (2) relatively narrow broad emission lines and (3) modest equivalent widths, as expected because of the occurrence of jet emission at very low inclination angles. In a disc-like sketch of the broad-line region, these results indicate a pole-on view of a flat geometry in blazars. This consistently extends the orientation-dependent unified model of active nuclei to the geometry of the broad-line region.