  We calculate the conductance of a two-dimensional bilayer with inverted
electron-hole bands, to study the sensitivity of the quantum spin Hall
insulator (with helical edge conduction) to the combination of electrostatic
disorder and a perpendicular magnetic field. The characteristic breakdown field
for helical edge conduction splits into two fields with increasing disorder, a
field $B_{c}$ for the transition into a quantum Hall insulator (supporting
chiral edge conduction) and a smaller field $B'_{c}$ for the transition to bulk
conduction in a quasi-metallic regime. The spatial separation of the inverted
bands, typical for broken-gap InAs/GaSb quantum wells, is essential for the
magnetic-field induced bulk conduction --- there is no such regime in HgTe
quantum wells.
