A two-dimensional nonlinear lattice model of austenite-martensite transformation is considered. The model Hamiltonian contains a periodic term and gradient ones. The mixed gradient terms are included to account for the coupling of internal structural degrees of freedom of the complex lattice with the conventional acoustic displacements. The exact solutions that describe constant velocity growth and morphology of the coexisting incommensurate austenite-martensite structures are obtained. In particular, the results explain the appearance so called "premartensitic" superlattice reflections that are typically observed near the transformations.