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In this paper, we theoretically analyze optically-induced transparency and absorption properties of a weak probe field in a two-mode coupled micro-cavity system and explore the tunable asymmetric Fano line shape of the transmission rates of the probe field. Both the modes in our system consist of an optical Kerr medium, one of them being passive while the other mode can be either active or passive. The forward transmission and backward reflection profile of the probe field are investigated for both passive–passive and passive–active cavity systems by varying different system parameters such as probe field detuning, photon tunneling strength, gain-to-loss ratio, etc. The results of this study have the potential to be applied in construction of quantum telecommunication and photonic devices. [ABSTRACT FROM AUTHOR]