Purpose: To accelerate 3D whole-heart joint T1/T2 mapping for myocardial tissue characterization using an end-to-end deep learning algorithm for joint motion estimation and model-based motion-corrected reconstruction of multi-contrast undersampled data. Methods: A free-breathing high-resolution motion-compensated 3D joint T1/T2 water/fat sequence is employed. The sequence consists of the acquisition of four interleaved volumes with 2-echo encoding, resulting in eight volumes with different contrasts. An end-to-end non-rigid motion-corrected reconstruction network is used to estimate high quality motion-corrected reconstructions from the eight multi-contrast undersampled data for subsequent joint T1/T2 mapping. Reconstruction with the proposed approach was compared against state-of-theart motion-corrected HD-PROST reconstruction. Results: The proposed approach yields images with good visual agreement compared to the reference reconstructions. The comparison of the quantitative values in the T1 and T2 maps showed the absence of systematic errors, and a small bias of-6.35 ms and-1.8 ms, respectively. The proposed reconstruction time was 24 seconds in comparison to 2.5 hours with motion-corrected HD-PROST, resulting in a reconstruction speed-up of over 370 times. Conclusion: In conclusion, this study presents a promising method for efficient whole-heart myocardial tissue characterization. Specifically, the research highlights the potential of the multi-contrast end-to-end deep learning algorithm for joint motion estimation and model-based motion-corrected reconstruction of multi-contrast undersampled data. The findings underscore its ability to compute T1 and T2 values with good agreement when compared to the reference motion-corrected HD-PROST method, while substantially reducing reconstruction time.