We have performed an eight-band k · p model calculation on the current-voltage ͑I-V͒ curves associated with interband magnetotransport in a double-barrier broken-gap heterostructure using the Burt-Foreman multiband envelope function theory and the scattering matrix approach. In a sample with very thin barriers, the broadening ⌫ 0 of a virtual bound state with energy E 0 can be very large. Depending on the relative values of ⌫ 0 and ͉E 0 − E F ͉, where E F is the Fermi energy, the behavior of the I-V curve can be either of Ohmic type or of resonant-tunneling type, and can be tuned from one to the other by changing the applied magnetic-field strength.