  For the first time we have combined dispersion measures and emission measures
towards 38 pulsars at KNOWN distances from which we derived the mean electron
density in clouds, N_c, and their volume filling factor, F_v, averaged along
the line of sight. The emission measures were corrected for absorption by dust
and contributions from beyond the pulsar distance. Results: The scale height of
the electron layer for our sample is 0.93+/-0.13 kpc and the midplane electron
density is 0.023+/-0.004 cm^-3, in agreement with earlier results. The average
density along the line of sight is <n_e> = 0.018+/-0.002 cm^-3 and nearly
constant. Since <n_e> = F_v N_c, an inverse relationship between F_v and N_c is
expected. We find F_v(N_c) = (0.011+/-0.003) N_c^{-1.20+/-0.13}, which holds
for the ranges N_c = 0.05-1 cm^-3 and F_v = 0.4-0.01. Near the Galactic plane
the dependence of F_v on N_c is significantly stronger than away from the
plane. F_v does not systematically change along or perpendicular to the
Galactic plane, but the spread about the mean value of 0.08+/-0.02 is
considerable. Conclusions: The inverse F_v-N_c relation is consistent with a
hierarchical, fractal density distribution in the diffuse ionized gas (DIG)
caused by turbulence. The observed near constancy of <n_e> then is a signature
of fractal structure in the ionized medium, which is most pronounced outside
the thin disk.
