The mechanical properties of polymer materials are intricately linked to their curing process. This relationship highlights the need for full-field monitoring techniques to provide rich and reliable experimental data. Due to the irreversible nature of curing, current methods cannot repeatedly measure a unidirectional curing process to get comprehensive, multi-dimensional information. To overcome this, we propose a novel multimodal full-field curing monitoring method that combines fluorescence imaging and tomographic interferometry. This approach leverages the high-sensitivity, full-field measurement capabilities of fluorescence digital image correlation and phase-sensitive optical coherence tomography to simultaneously estimate full-field strain on both the polymer's surface and internal cross-section during curing. We validated this by building a multimodal monitoring system with parallel channels for near-ultraviolet fluorescence excitation, blue fluorescence speckle imaging, and near-infrared tomographic imaging. Using backside illumination, we comprehensively monitored the curing of CharmFil Flow. During data acquisition, we calculated image correlations from fluorescence speckle to monitor full-field surface strain in the x-y plane. We then applied image correlation to tomographic results for internal transverse full-field strain along the x-direction in the x-z plane and used differential phase analysis for internal z-axis longitudinal full-field strain in the same plane. The consistency of our multimodal curing monitoring results was further confirmed by quantitatively characterizing time-domain shrinkage deformation across multiple dimensions. In essence, our method effectively achieves simultaneous multimodal full-field monitoring of both surface and internal polymer curing, offering a comprehensive and reliable measurement tool for in-depth studies of polymer curing dynamics and optimization of curing parameters.