This paper presents an integrated photonic platform for generating and parallel processing quantum frequency combs (QFCs). Cavity-enhanced parametric down-conversion with a Sagnac configuration generates QFCs with identical spectral distributions. On-chip quantum interference of different frequency modes is achieved simultaneously using the same photonic circuit, maintaining high interference visibility across all modes. This allows on-chip QFC reconfiguration and demonstration of a high-dimensional Hong-Ou-Mandel effect. The platform is a significant step towards efficient quantum information processing using integrated photonics and the frequency degree of freedom.