By application of the cleaved-edge overgrowth technique, we realize a two-channel superlattice (SL) device. The structure combines the parallel transport through a low-density SL under almost homogeneous electric field conditions with that through a surface SL (SSL) with large carrier density, which is, without parallel transport, subject to pronounced field instabilities. Direct control of the SSL density allows a separation of both transport contributions. With parallel transport through the low-density SL, the current carried by the SSL is characteristic for a SL with homogeneous field distribution. In particular, it exhibits negative differential conductivity over a wide range of applied electric fields. In contrast, for current only through the SSL clear electric-field instabilities, typical for SLs at high densities are observed. Thus, by means of the parallel transport channel, field instabilities are avoided and transport in high-density SLs with a homogeneous field distribution becomes accessible. (c) 2005 American Institute of Physics.