In this paper we investigated the response of a fiber-optic Fabry-Pérot sensing interferometer with thin ZnO layers deposited on the end faces of the optical fibers forming the cavity. Standard telecommunication single-mode optical fiber (SMF-28) segments were used with the thin ZnO layers deposited by Atomic Layer Deposition (ALD). Measurements were performed with the interferometer illuminated by two broadband sources operating at 1300 nm and 1550 nm. Reflected interference signal was acquired by an optical spectrum analyzer while the length of the air cavity was varied. Thickness of the ZnO layers used in the experiments was 50 nm, 100 nm, and 200 nm. Uncoated SMF-28 fiber was also used as a reference. Based on the results of measurements, the thickness of the ZnO layers and the length of the cavity were selected in order to achieve good visibility. Following, the interferometer was used to determine the refractive index of selected liquids.