Multi-material additive manufacturing is receiving growing attention in the field of acoustics, in particular for the design of micro-architectured periodic media used to obtain programmable ultrasonic responses. In this context, there is a need to develop wave propagation models to predict and optimize the impact of both the material properties and the spatial arrangement of the printed constituents. This work aims to investigate the transmission of longitudinal ultrasonic waves through periodic biphasic media that display viscoelastic constituent material properties. Thereby, we apply Bloch-Floquet analysis to unravel the relative contributions of viscoelasticity and periodicity on ultrasonic signatures, such as dispersion, attenuation, and bandgap characteristics. The impact of the finite size of such structures is also assessed by comparing the results from Bloch-Floquet analysis to those obtained using a transfer matrix formalism. The modelling outcomes, expressed in terms of frequency-dependent phase velocity and attenuation, are finally compared with experiments carried out on 3D-printed samples, which exhibit a 1D or 2D periodicity at a few hundred of micrometres length-scale. Altogether, the results provide insights into the modelling characteristics that must be accounted for to accurately predict the complex acoustic behaviour of periodic media in the ultrasonic regime.