Proper prediction of rainfall continues to be important in agricultural planning, water resource management and climate adaptation plans. Conventional statistical tools have difficulties in dealing with the non-linear non-stationary nature of rainfall time series. This research work is a hybrid deep learning model that combines Wavelet-ARIMA, CEEMDAN-LSTM, and CNN-BiLSTM models to forecast monthly rainfall on the basis of 44 years (1980-2024) of past data. Wavelet and CEEMDAN approaches separate inherent oscillatory patterns and minimize noise, as well as retain the time dynamics. Long-term dependencies are integrated in LSTM networks, whereas CNN-BiLSTM is able to obtain spatial-temporal features via bidirectional learning. Comparative studies demonstrate that, CEEMDAN-LSTM performs well with RMSE =0.11, MAE=0.08, R=0.80, followed by CNN-BiLSTM achieving RMSE=0.11, MAE=0.07, R=0.79, which is a lot better than Wavelet-ARIMA attaining RMSE=0.25, MAE=0.17, R=0.00. The reliability of the model is checked by residual analysis and correlation heatmaps, which allows interpreting the features. Findings indicate that adaptive signal decomposition methods with recurrent neural architecture can significantly improve forecasting precision in complex meteorological forecasting tasks, which has a practical implication of planning the resilience of regions to climate change.