In this paper, a (2 + 1)-dimensional nonlinear evolution equation generated via the Jaulent-Miodek hierarchy is investigated. Based on the Bell polynomials and Hirota method, bilinear forms and Backlund transformations are derived. One- and two-soliton solutions are constructed via symbolic computation. Soliton solutions are obtained through the Backlund transformations. We can get three types by choosing different parameters: the kink, bell-shape, and anti-bell-shape solitons. Propagation of the one soliton and elastic interactions between the two solitons are discussed graphically. After the interaction of the two bell-shape or anti-bell-shape solitons, solitonic shapes and amplitudes keep invariant except for some phase shifts, while after the interaction of the kink soliton and anti-bell-shape soliton, the anti-bell-shape soliton turns into a bell-shape one, and the kink soliton keeps its shape, with their amplitudes unchanged.