A new model for lamellar surfaces formed by anisotropic molecules is proposed. The molecules have internal degrees of freedom, associated with their flexible section of length N at zero temperature. We obtain a 2D non-standard six vertex model, which is exactly soluble and exhibits a finite order transition. The order and the character of the transition are determined by the dominant term in the 1 N-expansion of the interaction energy. The dependence of the critical temperatures on N is,

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... , determined by the non-leading terms in the same expansion.