Interferometry is one of the most widely used investigative techniques in various fields. With the implementation of interferometry on optical fibers, fiber optic interferometers (FOIs) have gained tremendous growth and advancement in the past four decades and have been explored for measurements of a diverse array of physical, chemical, and biological parameters. FOIs are typically constructed using single-mode fibers (SMFs) and are interrogated in the optical domain using probing light with a tightly controlled state of polarization (SOP), to ensure high-quality interference signals that facilitate sensing applications. The stringent requirement on the single-mode operation, as well as SOP, has hindered the further development of FOIs, for example, multimode fiber (MMF)-based FOIs. In this article, we present a comprehensive study of optical fiber-based microwave-photonic interferometers, which are based on a recently developed technique, optical carrier-based microwave interferometry (OCMI). The proposed sensing configuration enabled by the OCMI interrogation, namely, the microwave-photonic interferometer, essentially overcomes the two limiting aspects of traditional FOIs by reading FOIs in the microwave domain. The microwave-photonic interferometers are immune to variations of the SOP of the optical carrier and have low dependence on the types of optical fibers (SMFs and MMFs). We present a complete mathematical model of the microwave-photonic interferometric system. Then, the system is validated using three different types of interferometers, including the Mach-Zehnder interferometer, the Fabry-Perot interferometer, and the Michelson interferometer, based on both SMFs and MMFs. The sensing capability of the proposed system is verified for strain measurements using SMF and a multimode polymer optical fiber. The microwave-photonic interferometric configuration might pave the pathway forward for further expansion of FOIs in various sensing applications.