This study evaluates the dynamic modulus of Cold In-Place Recycling with Foamed Bitumen (FB-CIR) pavements, focusing on the influence of various recycled materials—reclaimed asphalt pavement (RAP), reclaimed inorganic binder stabilized aggregate (RAI), and their combination (RAP+RAI). Core samples from three representative FB-CIR projects in China were tested using the MTS-130 system across temperatures of −10°C, 5°C, 20°C, 35°C, and 50°C, and frequencies ranging from 25 Hz to 0.1 Hz. Statistical analysis and the Sigmoidal model were employed to analyze the viscoelastic behavior and establish the master curve for the FB-CIR dynamic modulus. The dynamic modulus of the three FB-CIR mixtures showed pronounced frequency-dependence, decreasing with reduced frequencies, and exhibited temperature sensitivity, with lower values at elevated temperatures. FB-RAI consistently demonstrated higher modulus values due to the hydration of previously unhydrated cement particles, while FB-RAP and FB-RAP+RAI displayed lower values, as RAP behaves similarly to unbound granular material. The construction of the master curve, based on the time-temperature superposition principle, enhanced our understanding of FB-CIR mixtures' mechanical behavior and enabled accurate extrapolation of dynamic modulus values across diverse conditions. Furthermore, FB-RAI's narrow phase angle variation indicates its superior mechanical stability and reduced sensitivity to external changes, making it ideal for areas with extreme climate fluctuations or heavy traffic. The study also identified three distinct phase angle variation patterns in FB-CIR mixtures, underscoring the importance of nuanced pavement design strategies that consider temperature, frequency, and material composition to optimize the performance and durability of FB-CIR pavements.