To address the problems of narrow frequency bands and significant barriers posed by bistable potential wells in piezoelectric energy harvesting with single cantilever beams, a novel solution is proposed by utilizing the bistable piezoelectric energy harvester employing magnetic attraction and repulsion between upper and lower beams. Firstly, a bistable structure with mutually-excited upper and lower beams and externally fixed magnets is constructed to broaden the vibration response and operational frequency range of the structure. By modeling the magnets as magnetic dipoles and establishing a planar magnetic force model, the impact of different parameters on the structural potential energy and magnetic force are determined. Subsequently, based on Euler-Bernoulli beam theory and Lagrangian equations, a comprehensive dynamic model of the system is formulated to analyze the influence of dynamic characteristics on the system. Experimental results show that, compared with the single upper or lower beams without fixed magnets, the proposed bistable piezoelectric energy harvester with magnetic attraction and repulsion expands the operational frequency range of the upper cantilever beam from 5~6 Hz to 3~11 Hz, resulting in a 26.35% increase in average power output within the 3~11 Hz band. Similarly, the operational frequency range of the lower cantilever beam is extended from 13~14 Hz to 4~13 Hz, with a 23.28% enhancement in average power output within the 4~13 Hz range.