We report an experimental study of miniband magnetoconduction in semiconducting InAs/GaSb superlattices. For samples with miniband widths below the longitudinal optical phonon energy we identify a new superlattice magnetophonon resonance (SLMPR) caused by resonant scattering of electrons across the mini-Brillouin zone. This new resonant feature arises directly from the drift velocity characteristics of the superlattice dispersion and total magnetic quantisation of the superlattice Landau level minibands. ; Comment: 9 pages, 8 figures, submitted to Phys. Rev. B