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Planar semiconductor microcavities in the strong light-matter coupling regime have recently emerged as a platform to realize strong optical nonlinearities in low-density limits. The 2D nature of transition metal dichalcogenides makes them ideal candidates to be integrated into a microcavity that can host exciton-polaritons. Among different excitations supported by different TMDCs, a prime candidate is the charge transfer excitons that form in heterobilayer TMDCs. Due to the spatial separation of the electron and holes into different layers, they have a permanent dipole moment which is expected to form dipolar polaritons with very high nonlinearities. However, due to a pure vertical dipole moment, the oscillator strength is small and hence can not be strongly coupled to microcavity photons. In principle, these problems can be circumvented in a suitable bilayer interlayer exciton system. Here, we report the strong coupling of interlayer excitons hosted by bilayer MoS$_2$ with the photonic modes supported by a microcavity. This is possible because the interlayer exciton in bilayer MoS$_2$ is an admixture of the charge transfer exciton and intralayer B exciton. Due to the mixing with B exciton, the interlayer exciton has a sizable oscillator strength which is enough to strongly couple it with the cavity photon. We observe a 10 fold increase in nonlinearity for the interlayer exciton compared to the A exciton-polariton in low-density limit. We also separate the contributions of the exciton-exciton interaction and saturation due to phase space filling from the observed nonlinearity.