In this work, we study the evolution of a spatially flat Universe by considering a viscous dark matter and perfect fluids for dark energy and radiation, including an interaction term between dark matter and dark energy. In the first part, we analyze the general properties of the Universe by performing a stability analysis, and then we constrain the free parameters of the model using the latest and cosmological-independent measurements of the Hubble parameter. We find consistency between the viscosity coefficient and the condition imposed by the second law of the thermodynamics. The second part is dedicated to constraining the free parameter of the interacting viscous model (IVM) for three particular cases: the viscous model (VM), interacting model (IM), and the perfect fluid case [Lambda-Cold Dark Matter (LCDM)]. We report the deceleration parameters as q0=-0.5 4-0.05+0.06, -0.5 8-0.04+0.05 , -0.5 8-0.05+0.05 , and -0.6 3-0.02+0.02 , together with the jerk parameters as j0=0.8 7-0.09+0.06 , 0.94-0.06+0.04 , 0.91-0.10+0.06 , and 1.0 for the IVM, VM, IM, and LCDM respectively, where the uncertainties correspond at 68% confidence level. It is worth mentioning that all the particular cases are in good agreement with LCDM, in some cases producing even better fits, with the advantage of eliminating some problems that afflict the standard cosmological model.