Recent advances in additive manufacturing of viscoelastic materials have paved the way towards the design of increasingly complex multi-material structures with heterogeneities from the micro- to the macroscale. However, the measurement of ultrasound characteristics in such viscoelastic structures is a challenging problem, due to the strong attenuation related to both the constituent materials and the architecture. We propose here a methodological framework to identify the phase velocity and attenuation in viscoelastic multi-material quasi-heterogeneous samples. The proposed approach relies on measurements achieved in double through-transmission at various incidence angles, referred as theta-scan. The forward modeling of the wave propagation in such media allows then to identify the ultrasound characteristics based on an inverse approach. Experiments were performed on multi-material samples made of a random pattern of inclusions of a soft elastomer inside a rigid glassy polymer. The effects of the volume fraction of the constituent materials on the ultrasound characteristics was evaluated. This methodology open the path towards ultrasonic measurements in highly attenuating architectures