We investigate discrete integrable systems within the framework of the difference variational bicomplex, using the formalism of Lagrangian multiforms, which generalize classical volume forms. This approach provides a geometric and variational foundation for integrability, with a focus on the multidimensional consistency of discrete equations. By constructing Lagrangian multiforms on the bicomplex, we establish a unified variational principle that naturally accommodates multiple directions in the discrete independent variables. The structure of the variational bicomplex enables a systematic derivation of multiform Euler–Lagrange equations, shedding light on the underlying cohomological structure of discrete integrable systems.