We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: V2 + D2 = P2, involves three measures, visibility V, distinguishability D, and the degree of polarization P, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT: V2 + D2 ≤ 1, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects.