This work aims to propose a well-balanced and positivity-preserving numerical scheme for the two-dimensional two-layer shallow water equations with a nonflat bottom topography on uniform meshes. One difficulty is to preserve the water at rest when the computational domain contains wet–dry fronts. It is highly nontrivial. Another difficulty in solving the system is to deal with the nonconservative product term which cannot be defined in the distributional sense. To overcome these issues, we define auxiliary interface variables motivated by the generalized hydrostatic reconstruction (Castro et al., 2007) for computing Riemann states to obtain consistent numerical fluxes across the cell interface. When the water is at rest, the numerical flux should be continuous across the cell interface and the nonconservative product term is equivalent to the gradient of physical fluxes. In order to maintain steady states at a discrete level, we discretize the integral of the source term in the upwind sense. One of the main contributions of this work is to introduce a monotone-preserving reconstruction for constructing non-oscillatory piecewise linear polynomials to improve the accuracy in space. The current scheme can guarantee both layer heights to be nonnegative and maintain the water at rest even if the computational domain contains wet–dry fronts. Several numerical results indicate that the current scheme is stable in solving the two-dimensional two-layer shallow water equations with wet–dry fronts. In particular, the current scheme is stable when computing complicated states which contain many shocks and will evolve to a turbulent state.