We present ring resonator (RR)-coupled Mach-Zehnder interferometers (MZIs) based on silicon-on-insulator rib waveguides, operating around the mid-IR wavelength of 3.8 μm. A number of different photonic integrated devices have been designed and fabricated experimentally to obtain the asymmetric Fano resonances in the mid-IR. We have investigated the influence of the coupling efficiency between the RR and the MZI as well as the phase shift between the two arms of the MZI on the Fano-type resonance spectral features, in agreement with theoretical predictions. Finally, wavelength-dependent Fano transmittances have been successfully measured with insertion losses up to ∼1 dB and extinction ratios of ∼20 dB. A slope of sharp Fano resonances as high as -574.6/μm has been achieved and estimated to be 35.5% higher than the slope of single RR Lorentzian-type resonances.