Linear stability of shallow flows is usually analyzed in the literature under the assumption that the base flow profile is symmetric with respect to the transverse coordinate. Another widely used assumption is the rigid-lid assumption where perturbations at the upper surface are not considered. Experimental data show that the symmetry of the base flow can be distorted by a non-uniform friction in the transverse direction of the flow. Such a situation occurs in applications in case of the presence of aquatic vegetation (for example, in case of floods). In this case there is a sharp change of the resistance force at the interface. Experiments show that nonuniform resistance force plays an important role in development of the mixing layer. In the present paper linear stability analysis of shallow mixing layers with non-uniform friction is investigated. Both previously mentioned assumptions are removed and the problem is solved for asymmetric base flow profile for arbitrary Froude numbers. The friction coefficient is assumed to be a function of the transverse coordinate. Experimentally measured asymmetric base flow profile is used in the paper. The linear stability problem is solved numerically by a collocation method based on Chebyshev polynomials using different values of the parameters of the problem.