Particle-scale understanding of soft (tyre particles) and rigid (crushed rock) granular mixes is essential in predicting their geo-mechanical response. Their numerical simulation using Discrete Element Method (DEM) to explore particle-scale mechanics necessitates development of a coherent contact model, especially when employing spherical particles. Previous studies have utilized various contact models that fall short in accurately simulating the macroscopic behaviour of these unconventional mixtures. To address this limitation, a combination of Hertz-Mindlin contact with linear rolling resistance is implemented. This contact model takes into account the nonlinear stiffness variation of soft and rigid particles with increasing load level and incorporates particle shape effects. The study focuses on the 1D compression response of samples with varying soft fractions. Calibration between experimental and numerical data, based on macroscopic quantities (void ratio, constrained modulus), demonstrate strong agreement. The study delves into evolution of various particle-scale parameters, including coordination numbers, contact force, orientation biases and lateral pressure. Results reveal the transition of microstructural features with increasing soft content as loading progresses and indicate that soft particles arrest sliding and rotation due to greater inter-particle overlap compared to rigid particles. Therefore, with increasing soft content, the contact force demonstrates a tendency to transfer through soft-rigid contacts.