Accurate and noninvasive blood pressure (BP) monitoring is essential for managing cardiovascular health, yet traditional cuff-based methods are uncomfortable and unsuitable for continuous use. Existing cuffless BP estimation techniques face limitations such as limited feature extraction capabilities, which can result in lower performance, and validation on nonstandard or small datasets, which raises concerns about generalizability. To address these challenges, we propose a novel convolutional neural network (CNN)-long short-term memory (LSTM) architecture that independently processes photoplethysmogram (PPG) and electrocardiogram (ECG) signals through separate CNN layers, enhancing morphological feature extraction. These layers are followed by a multilayer Bi-LSTM network that captures long-term temporal dependencies, improving BP prediction accuracy. Unlike prior studies, we validate our method on the PulseDB dataset, the largest publicly available dataset for BP estimation, comprising cleaned PPG, ECG, and arterial BP (ABP) waveforms from the MIMIC-III and VitalDB databases. Evaluated on data from 3027 individuals using fivefold cross-validation, our model achieved a mean absolute error (MAE) of 5.16 mmHg for systolic BP (SBP) and 3.24 mmHg for diastolic BP (DBP), with consistent performance across various age groups and genders. These results surpassed American National Standards Institute (ANSI)/Association for the Advancement of Medical Instrumentation (AAMI) standards and achieved an "A" grade by British Hypertension Society (BHS) standards, demonstrating the potential of this approach to improve patient comfort and care in diverse clinical and home environments.