The insertion loss and extinction ratio of an amplitude modulator and a 2×2 switch based on a two-mode fiber (TMF) interferometer butt coupled to one or two offset single-mode fibers are analyzed theoretically. Performance is shown to be limited by the asymmetric shape and small secondary lobe of the TMF mode pattern, which prevent full coupling to the single-mode fiber. For an amplitude modulator using a circular (elliptical) core TMF, applying a suitable offset between fibers and optimizing the fiber parameters, the loss can be minimized to 0.39 dB (0.23 dB); the extinction ratio is then 14.4 dB (16.9 dB). With a different offset, the extinction ratio can be made infinite, but the loss is then 0.95 dB (0.47 dB). Comparable figures are derived for a switch.