This study introduces an innovative deep-learning model for cuffless blood pressure estimation using PPG and ECG signals, demonstrating state-of-the-art performance on the largest clean dataset, PulseDB. The rU-Net architecture, a fusion of U-Net and ResNet, enhances both generalization and feature extraction accuracy. Accurate multi-scale feature capture is facilitated by short-time Fourier transform (STFT) time-frequency distributions and multi-head attention mechanisms, allowing data-driven feature selection. The inclusion of demographic parameters as supervisory information further elevates performance. On the calibration-based dataset, our model excels, achieving outstanding accuracy (SBP MAE ± std: 4.49 ± 4.86 mmHg, DBP MAE ± std: 2.69 ± 3.10 mmHg), surpassing AAMI standards and earning a BHS Grade A rating. Addressing the challenge of calibration-free data, we propose a fine-tuning-based transfer learning approach. Remarkably, with only 10% data transfer, our model attains exceptional accuracy (SBP MAE ± std: 4.14 ± 5.01 mmHg, DBP MAE ± std: 2.48 ± 2.93 mmHg). This study sets the stage for the development of highly accurate and reliable wearable cuffless blood pressure monitoring devices.