Despite intense research into the optoelectronic properties of metal halide perovskites (MHPs), sub-bandgap absorption in MHPs remains largely unexplored. Here we recorded two-photon absorption spectra of MHPs using the time-resolved microwave conductivity technique. A two-step upward trend is observed in the two-photon absorption spectrum for methylammonium lead iodide, and some analogues, which implies that the commonly used scaling law is not applicable to MHPs. This aspect is further confirmed by temperature-dependent conductivity measurements. Using an empirical multiband tight binding model, spectra for methylammonium lead iodide were calculated by integration over the entire Brillouin zone, showing compelling similarity with experimental results. We conclude that the second upward trend in the two-photon absorption spectrum originates from additional optical transitions to the heavy and light electron bands formed by the strong spin-orbit coupling. Hence, valuable insight can be obtained in the opto-electronic properties of MHPs by sub-bandgap spectroscopy, complemented by modelling.