Electronic Mach-Zehnder interferometers were constructed recently from chiral one-dimensional integer quantum Hall edge states. These interferometers showed an unexpected behavior of the visibility of Aharonov-Bohm (AB) oscillations in the nonlinear regime, where the visibility developed a lobe structure accompanied by the $pi$-jumps of the AB-phase [1]. We address these phenomena by studying the model of a Mach-Zehnder interferometer, where the one-dimensional electrons interact via long-range potential. We calculate exactly the visibility of the Aharonov-Bohm oscillations in this model, which agrees well with experimental results. [1] "Unexpected Behavior in a Two-Path Electron Interferometer", I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, and V. Umansky, Phys. Rev. Lett. 96, 016804, (2006)