Highly accurate interval forecasting of electricity demand is fundamental to the success of reducing the risk when making power system planning and operational decisions by providing a range rather than point estimation. In this study, a novel modeling framework integrating bivariate empirical mode decomposition (BEMD) and support vector regression (SVR), extended from the well-established empirical mode decomposition (EMD) based time series modeling framework in the energy demand forecasting literature, is proposed for interval forecasting of electricity demand. The novelty of this study arises from the employment of BEMD, a new extension of classical empirical model decomposition (EMD) destined to handle bivariate time series treated as complex-valued time series, as decomposition method instead of classical EMD only capable of decomposing one-dimensional single-valued time series. This proposed modeling framework is endowed with BEMD to decompose simultaneously both the lower and upper bounds time series, constructed in forms of complex-valued time series, of electricity demand on a monthly per hour basis, resulting in capturing the potential interrelationship between lower and upper bounds. The proposed modeling framework is justified with monthly interval-valued electricity demand data per hour in Pennsylvania-New Jersey-Maryland Interconnection, indicating it as a promising method for interval-valued electricity demand forecasting.