We present infrared spectrophotometry of the Pa alpha (n = 4-3) emissi
on line of hydrogen, together with optical spectrophotometry of H alph
a and H beta, of a flux-limited sample of 11 radio sources. The sample
consists of all FR II 3CR radio sources with 0.1 less than or equal t
o z < 0.2 and 5(h) < R.A. < 16(h) which contains eight narrow-line rad
io galaxies (3CR 135, 184.1, 219, 223, 236, 319, 321, and 327), two br
oad-line radio galaxies (3CR 234 and 3CR 303), and one quasar (3CR 273
). The observations were aimed at the detection of obscured broad line
s, hidden from our view by dust absorption, as a means of testing theo
ries of the unification of radio galaxies and quasars. All the objects
except 3CR 236 and 3CR 273 show significant reddening of the narrow a
nd broad lines, typically of order A(V) similar to 1.5 for narrow line
s and similar to 3 for broad lines. We detect highly obscured broad-li
ne regions in 3CR 184.1, 219, and 223, which appear to be narrow-line
objects in the optical, so these should be reclassified as broad-line
radio galaxies. In all cases except 3CR 273 and 3CR 303, the broad lin
es are reddened more than the narrow lines, locating much of the dust
responsible for absorbing the broad-line emission between the broad- a
nd narrow-line regions. The dereddened line luminosities range up to t
hose of low-luminosity quasars. The results are broadly consistent wit
h models which seek to unify radio galaxies and quasars through orient
ation, where an axisymmetric equatorial obscuring region hides the qua
sar nucleus from view unless the radio axis is pointing close to our l
ine of sight. These data provide the first opportunity to model the di
stribution of broad-line region extinctions in a complete sample, rath
er than model just the fraction of quasars and radio galaxies. We deve
lop a simple unification model that matches the observed distribution
of extinctions, explains our observations, and makes predictions about
the fraction of obscured quasars that will be present in samples of h
igher radio luminosity.