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Three-dimensional bioprinting has emerged as a promising technique in tissue engineering applications through the precise deposition of cells and biomaterials in a layer-by-layer fashion. However, the limited availability of hydrogel bioinks is frequently cited as a major issue for the advancement of cell-based extrusion bioprinting technologies. It is well known that highly viscous materials maintain their structure better, but also have decreased cell viability due to the higher forces which are required for extrusion. However, little is known about the effect of the two distinct components of dynamic modulus of viscoelastic materials, storage modulus (G') and loss modulus (G″), on the printability of hydrogel-based bioinks. Additionally, 'printability' has been poorly defined in the literature, mostly consisting of gross qualitative measures which do not allow for direct comparison of bioinks. This study developed a framework for evaluating printability and investigated the effect of dynamic modulus, including storage modulus (G'), loss modulus (G″), and loss tangent (G″/G') on the printing outcome. Gelatin and alginate as model hydrogels were mixed at various concentrations to obtain hydrogel formulations with a wide range of storage and loss moduli. These formulations were then evaluated for the quantitatively defined values of extrudability, extrusion uniformity, and structural integrity. For extrudability, increasing either the loss or storage modulus increased the pressure required to extrude the bioink. A mathematical model relating the G' and G″ to the required extrusion pressure was derived based on the data. A lower loss tangent was correlated with increased structural integrity while a higher loss tangent correlated with increased extrusion uniformity. Gelatin-alginate composite hydrogels with a loss tangent in the range of 0.25-0.45 exhibited an excellent compromise between structural integrity and extrusion uniformity. In addition to the characterization of a common bioink, the methodology introduced in this paper could also be used to evaluate the printability of other bioinks in the future.