  Multimode integrated interferometers have great potential for both spectral
engineering and metrological applications. However, material dispersion of
integrated platforms constitutes an obstacle which limits the performance and
precision of such interferometers. At the same time, two-colour non-linear
interferometers present an important tool for metrological applications, when
measurements in a certain frequency range are difficult. In this manuscript, we
theoretically develop and investigate an integrated multimode two-colour
SU(1,1) interferometer that operates in a supersensitive mode. By ensuring a
proper design of the integrated platform, we suppress dispersion and thereby
significantly increase the visibility of the interference pattern. We
demonstrate that such an interferometer overcomes the classical phase
sensitivity limit for wide parametric gain ranges, when up to $3*10^4$ photons
are generated.
