Cleavage refraction angles are used to estimate effective viscosity contrasts between interlayered quartzites and phyllites within the Baraboo Syncline, Wisconsin, USA. Both types of layers contain two major phases, quartz and pyrophyllite, with minor amounts of hematite. Quartz (with minor hematite) behaves as the strong phase and pyrophyllite acts as the weak phase. Cleavage refraction directly relates to mineralogy with a linear relationship between bedding/cleavage angle and strong-phase concentration. Mineralogy exerts first-order control over effective viscosity contrasts, which are generally small, in most cases <10. Effective viscosity contrasts are consistent across the fold, so are likely not to be highly strain dependent and indicate approximate linear viscous rheology. Microstructures suggest deformation was dominated by dislocation creep in layers with high quartz concentrations and diffusive mass transfer in layers with lower quartz concentrations, and that the transition of the deformation mechanism is gradual. Thus, the rheological flow laws at the small scale may not reflect the bulk flow law at the large scale over the span of the deformation. Effective viscosity contrasts allow an evaluation of samples compared to theoretical two-phase mixtures. The analysed samples most closely resemble the Reuss bound of two-phase mixtures, regardless of the mineralogy.