Context. A currently unsolved question in supernova research is the origin of stripped-envelope supernovae (SESNe). Such SNe lack spectral signatures of hydrogen (Type Ib), or hydrogen and helium (Type Ic), indicating that the outer stellar layers have been stripped during their evolution. The mechanism for this is not well understood, and to disentangle the different scenarios determination of nucleosynthesis yields from observed spectra can be attempted. However, the interpretation of observations depends on the adopted spectral models. A previously missing ingredient in these is the inclusion of molecular effects, which can be significant. Aims. We aim to investigate how the molecular chemistry in stripped-envelope supernovae affect physical conditions and optical spectra, and produce ro-vibrational emission in the mid-infrared (MIR). We also aim to assess the diagnostic potential of observations of such MIR emission with JWST. Methods. We couple a chemical kinetic network including carbon, oxygen, silicon, and sulfur-bearing molecules into the NLTE spectral synthesis code SUMO. We let four species -CO, SiO, SiS and SO -participate in the NLTE cooling of the gas to achieve self-consistency between the molecule formation and the temperature. We apply the new framework to model the spectrum of a Type Ic supernova in the 100-600d time range. Results. Molecules are predicted to form in SESN ejecta in significant quantities (typical mass 10 −3 M ) throughout the 100-600d interval. The impact on the temperature and optical emission depends on the density of the oxygen zones and varies with epoch. For example, the [O I] 6300, 6364 feature can be quenched by molecules from 200 to 450d depending on density. The MIR predictions show strong emission in the fundamental bands of CO, SiO, and SiS, and in the CO and SiO overtones. Conclusions. Type Ibc SN ejecta have rich chemistry and consideration of the effect of molecules is important for modeling the temperature and atomic emission in the nebular phase. Observations of stripped-envelope supernovae with JWST hold promise to provide the first detections of SiS and SO, and to give information on zone masses and densities of the ejecta. Combined optical, near-infrared, and mid-infrared observations can break degeneracies and achieve a more complete picture of the nucleosynthesis and chemistry of Type Ibc SNe.