We investigate a two-species Fermi gas in which one species is
confined in a two-dimensional plane (2D) or one-dimensional line (1D)
while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351<m2D/m3D < 6.35 for the 2D-3D mixture or 0.00646<m1D/m3D < 2.06 for the 1D-3D mixture, the resulting system is stable against the Efimov effect and has universal properties. We calculate key quantities in the many-body phase diagram. Other possible scale-invariant systems with short-range few-body interactions are also elucidated.