  Let G be a Lie supergroup and H a closed subsupergroup. We study the
unimodularity of the homogeneous supermanifold G/H, i.e. the existence of
G-invariant sections of its Berezinian line bundle. To that end, we express
this line bundle as a G-equivariant associated bundle of the principal H-bundle
G over G/H. We also study the fibre integration of Berezinians on oriented
fibre bundles. As an application, we prove a formula of `Fubini' type: the
invariant integral over G can be expressed (up to sign) by a succesive
invariant integration over H and G/H. Moreover, we derive analogues of integral
formulae for the transformation under local isomorphisms of unimodular
homogeneous superspaces G/H and S/T, and under the products of subsupergroups
of Lie supergroups. The classical counterparts of these formulae have numerous
applications in harmonic analysis.
