We present measurements of the specific heat coefficient gamma (equivalent to C/T) in the low-temperature limit as a function of an applied magnetic field for the Fe-based superconductor BaFe2(As0.7P0.3)(2). We find both a linear regime at higher fields and a limiting square root H behavior at very low fields. The crossover from a Volovik-like root H to a linear field dependence can be understood from a multiband calculation in the quasiclassical approximation assuming gaps with different momentum dependence on the hole-and electronlike Fermi surface sheets.