We show that resonant tunneling of electromagnetic fields can occur through a three-layer structure composed of a single-negative (i.e., either negative permittivity or negative permeability) slab paired with a bilayer made of double-positive (i.e., positive permittivity and permeability) media. In particular, one of the two double-positive media can be chosen arbitrarily (even vacuum), while the other may exhibit extreme (either near-zero or very high) permittivity and permeability values. Our results on this counterintuitive tunneling phenomenon also demonstrate the possibility of synthesizing double-positive slabs that effectively exhibit single-negative-like wave-impedance properties within a moderately wide frequency range.