Light is neither wave nor particle, but both, according to Bohr’s complementarity principle, which was first devised to qualitatively characterize quantum phenomena. Later, quantification was achieved through inequalities such as V2 + D2 ≤ 1, which engage visibility V and distinguishability D. Recently, equality V2 + D2 = P2-the polarization coherence theorem (PCT)—was established, incorporating polarization P and addressing both quantum and classical coherences. This shows that Bohr’s complementarity is not restricted to quantum phenomena. We derive an extension of the PCT that also applies to quantum and classical light fields carrying intertwined, dichotomic observables, such as polarization and two-path alternative. We discuss how constraints critically depend on the chosen measurement strategy. This may prompt various experiments to exhibit complementary features that possibly lurk behind hidden coherences.