We propose modeling signed networks by considering two layers in a social network for generation of positive and negative links where both the layers comprise of identical set of nodes. The growth process is modeled based on preferential attachment, formation of links probabilistically asserting structural balance of local groups, and internal growth which happens without addition of new nodes. We prove that the degree distribution of a generated network follows a power-law whose exponent depends on the largest eigenvalue of a matrix which governs the dynamics of growth of degrees of nodes with respect to positive and negative links. A computable formula for average degree and lower-bounds for the number of balanced and unbalanced triads of modelled networks are also obtained. A method for structural reconstruction of real signed networks is formulated through estimation the values of the model parameters to generate the network that can inherit different structural properties of the corresponding real network. Experimental results show that our model which we term as 2L-SNM can replicate properties of several real world signed networks much more robustly than competitive state-of-the-art techniques.