The behavior of complex fluids inside porous media may be very different from when they are not.  This is a problem encountered in many biological or industrial applications ranging from impregnation of fibrous materials to immiscible multi-phase flow in porous media. Of all the different types of non-Newtonian fluids, many undergo behavioral changes depending on the stress or strain applied. One may cite  the Carreau rheology  which is Newtonian at low shear rate but behaves as a power law fluid above a certain shear rate. Another example is the yield stress fluid that responds as a solid below a critical stress and as a power law fluid above. At the mesocopic level, this rheological approach can also be extended to immiscible displacements in porous media. In this case, the fluids may each be Newtonian but the interfacial tension between them makes them effectively behave in a non-Newtonian way.  For instance, a minimum level of stress is required for a non-wetting phase to invade small pore throats. The local flow rate will then be different below and above this threshold. The purpose of this presentation is to study the coupling between the heterogeneities of a porous medium and a rheology with a change in behavior. We study a very simple model called bi-viscous, where the fluid is Newtonian but with a change in viscosity at a particular shear rate (or shear stress). The coupling between the disorder and such a simple rheological model leads to a very rich problem. In particular, two limit cases of this problem present universal behaviors sharing the universality class of percolation or the directed polymer problem (KPZ).