We critically re-examine existing empirical studies of vertical and horizontal statistics of the horizontal wind and find that the balance of evidence is in favour of the Kolmogorov k(x)(-5/3) scaling in the horizontal, Bolgiano-Obukov scaling k(z)(-11/5) in the vertical corresponding to a D(s) = 23/9 stratified atmosphere in (x, y, z) space. This interpretation is particularly compelling once one recognizes that the 23/9-D turbulence can lead to long-range biases in aircraft trajectories and hence to spurious statistical exponents in wind, temperature and other statistics reported in the literature. Indeed, we show quantitatively that one is easily able to reinterpret the major aircraft-based campaigns (GASP, MOZAIC) in terms of the model. In part I, we have seen that this model is compatible with 'turbulence waves' which can be close to classical linear gravity waves in spite of their very different nonlinear mechanism. We then use state-of-the-art lidar data of atmospheric aerosols (considered as passive tracers) in order to obtain direct estimates of the effective ('elliptical') dimension of the spatial part: D(s) = 23/9 = 2.55 +/- 0.02. This result essentially rules out the standard 3-D or 2-D isotropic theories or the anisotropic quasi-linear gravity wave theories which have D(s) = 3, 2, 7/3 respectively. In this paper we focus on the multifractal (intermittency) statistics showing that there is a very small but apparently real variation in the value of D(s), ranging for the weak and intense structures so that Ds ranges from roughly 2.53 to 2.57. We also show that the passive scalars are well approximated by universal multifractals; we estimate the exponents to be alpha(h) = 1.82 +/- 0.05, alpha(v) = 1.83 +/- 0.04, C(1h) = 0.037 +/- 0.0061 and C(1v) = 0.059 +/- 0.007 (h for horizontal, v for vertical). Copyright (c) 2008 Royal Meteorological Society.