We report on experiments and discrete element simulations of homogeneous, simple, normal stress-controlled, shear flows of model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid. The rheology of such unsaturated granular materials in the dense flow regime was characterized in recent publications of our group, in terms of internal friction coefficient μ∗ and solid fraction Φ, depending on the reduced pressure P∗ comparing capillary forces to controlled normal stress, and on inertial number I. The present study extends this description to the influence of the liquid viscosity on material rheology in the low saturation regime. The quantitative agreement of simulations with experiments is confirmed for the quasistatic limit, and our numerical results, despite some quantitative differences, capture the correct trends in the regime dominated by viscous forces. Rheological properties are then determined, to a large extent, by the same viscous numberIv as used to formulate constitutive laws in saturated, dense suspensions. More precisely, a visco-inertial numberJ, combining Iv with inertial number I as J=Iv+2I2, appears apt to describe the rheological laws, as expressed by the internal friction coefficient and the solid fraction, measured in the laboratory or in the simulations, as well as the numerically investigated internal state of the flowing material. Simulations provide insight into the role of viscous forces: predominantly tensile, they contribute to the increase with shear rate of the macroscopic friction coefficient μ∗ through a direct positive contribution to shear stress, a negative contribution to normal stresses (enhancing the strength of the contact network), and microstructural changes affecting the network of contacts and liquid bridges.