We look in detail at the multifractal scaling of the fluctuations in the interplanetary magnetic field strength as measured onboard Voyager 2 in the entire heliosphere and even in the heliosheath. More specifically, we analyse the spectra observed by Voyager 2 in a wide range of solar activity cycles during the years 1980–2009 at various heliospheric latitudes and distances from 6 to 90 astronomical units (AU). We focus on the singularity multifractal spectrum before and after crossing the termination heliospheric shock by Voyager 2 at 84 AU from the Sun. In addition, we investigate here the parameters of the model that describe the asymmetry of the spectrum, depending on the solar cycle. It is worth noting that the spectrum is prevalently right-skewed inside the whole heliosphere. Moreover, we have possibly observed a change in the asymmetry of the spectrum at the termination shock. We show that the degree of multifractality is modulated by the solar activity. Hence these basic results also bring significant support to some earlier claims suggesting that the solar wind termination shock is asymmetric.