  We report observation of a counter-intuitive phenomenon in multi-path
correlation interferometry with thermal light. The intensity correlation
between the outputs of two unbalanced Mach-Zehnder interferometers (UMZI) with
two classically correlated beams of thermal light at the input exhibits genuine
second-order interference with the visibility of $1/3$. Surprisingly, the
second-order interference does not degrade at all no matter how much the path
length difference in each UMZI is increased beyond the coherence length of the
thermal light. Moreover, the second-order interference is dependent on the
difference of the UMZI phases. These results differ substantially from those of
the entangled-photon Franson interferometer which exhibits two-photon
interference dependent on the sum of the UMZI phases and the interference
vanishes as the path length difference in each UMZI exceeds the coherence
length of the pump laser. Our work offers deeper insight into the interplay
between interference and coherence in multi-photon interferometry.
