Multi-material additive manufacturing is receiving increasing attention in the field of acoustics, in particular towards the design of micro-architectured periodic media used to achieve programmable ultrasonic responses. To unravel the effect of the material properties and spatial arrangement of the printed constituents, there is an unmet need in developing wave propagation models for prediction and optimization purposes. In this study, we propose to investigate the transmission of longitudinal ultrasound waves through 1D-periodic biphasic media, whose constituent materials are viscoelastic. To this end, Bloch–Floquet analysis is applied in the frame of viscoelasticity, with the aim of disentangling the relative contributions of viscoelasticity and periodicity on ultrasound signatures, such as dispersion, attenuation, and bandgaps localization. The impact of the finite size nature of these structures is then assessed by using a modeling approach based on the transfer matrix formalism. Finally, the modeling outcomes, i.e., frequency-dependent phase velocity and attenuation, are confronted with experiments conducted on 3D-printed samples, which exhibit a 1D periodicity at length-scales of a few hundreds of micrometers. Altogether, the obtained results shed light on the modeling characteristics to be considered when predicting the complex acoustic behavior of periodic media in the ultrasonic regime.