We demonstrate a first-order interference between coherent light at 1580 nm and 795 nm by using a frequency-domain Mach-Zehnder interferometer (MZI). The MZI is implemented by two frequency-domain BSs based on a second-order nonlinear optical effect in a periodically-poled lithium niobate waveguide with a strong pump light. The observed visibility is over 0.99 at 50% conversion efficiencies of the BSs. Toward photonic quantum information processing, sufficiently small background photon rate is necessary. From measurement results with a superconducting single photon detector (SSPD), we discuss the feasibility of the frequency-domain MZI in a quantum regime. Our estimation shows that the single photon interference with the visibility above 0.9 is feasible with practical settings.