In deregulated power markets, electricity price forecasting is the most valuable tool. However, with inherent electricity price characteristics, such as high frequency and volatility, constructing an electricity price forecasting model remains a difficult task for decision-makers and scholars. Accurate electricity price point forecasting (PF) can guide market participants in maximizing benefits. Moreover, appropriate interval forecasting (IF) can provide further information based on PF. Accordingly, a novel electricity price multi-bi-forecasting system using multivariable and multi-input multi-output structures is formulated. The system has three stages: data preprocessing, combination forecasting, and performance evaluation. The data preprocessing stage removes and smooths the high-frequency electricity price and load data. Because the load series has a more regular cycle and smoother fluctuation than the electricity price series, two variables, electricity price and load, are employed for forecasting using a multivariable data arrangement rolling forecast mechanism. In addition, a multi-input multi-output structure is utilized by three member models (back propagation, bidirectional long short-term memory, and gated recurrent unit) to derive PF and IF results concurrently. The final results are obtained using a combined strategy based on the multi-objective salp swarm algorithm. Finally, three experiments are conducted in the Australian electricity market to evaluate the proposed system quantitatively. Results show that the designed system has superior ability in forecasting electricity price and practical application in real situations.