The recent excitement about Dirac and Weyl fermion systems has renewed interest in magnetotransport properties of multicarrier systems. However, the complexity of their analysis, even in the simplest two-carrier case, has hampered a good understanding of the underlying phenomena. Here we propose a new analysis scheme for two independent conduction channels, that strongly reduces previous ambiguities and allows one to draw robust conclusions. This is demonstrated explicitly for the example of three-dimensional topological insulators. Their temperature and gate voltage-dependent Hall coefficient and transverse magnetoresistance behavior, including the phenomenon of huge linear transverse magnetoresistance, can be traced back to two conduction channels, with fully determined carrier concentrations and mobilities. We further derive an upper limit for the transverse magnetoresistance. Its violation implies field dependencies in the electronic band structure or scattering processes, or the presence of more than two effective carrier types. Remarkably, none of the three-dimensional topological insulators or semimetals with particularly large transverse magnetoresistance violates this limit.