Calibration of constitutive models for novel materials is a central challenge in computational mechanics, particularly for multiscale materials where key features emerge at length scales that are difficult to observe directly. Bayesian inference provides a rigorous framework for parameter identification and uncertainty quantification, but its application to realistic calibration problems is often limited by the slow convergence of sampling-based methods and the computational cost of modern PDE-governed models. This contribution investigates whether the recently developed Bayesian calibration framework based on piecewise-deterministic Markov process (PDMP) sampling can overcome these limitations in a realistic setting. The PDMP framework for posterior sampling is applied to a real-world materials characterization problem: the identification of constitutive parameters describing the interface transition zone surrounding aggregates in concrete. The interface transition zone is a microscale feature that strongly influences macroscopic behaviour, yet its mechanical properties remain largely uncharacterized. A higher-scale material model is considered in which elastic stiffness explicitly depends on the distance from aggregate surfaces, introducing a finite number of parameters governing the stiffness in the interface transition zone. A Bayesian inverse problem is formulated to calibrate these parameters from mechanical response data, yielding both parameter estimates and associated uncertainty. Efficient posterior sampling is achieved with the surrogate assisted PDMP methodology.