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.