A phase-field model for the phase transition between austenite and martensite and twinning between two martensitic variants is presented from our previous theory 1 with the main focus on the influence of interfacial stress that is consistent with the sharp interface limit. Each variant-variant transformation can be represented by only one order parameter. Thus, it allows us to get the analytical solution of interface energy and width. Coupled phase-field and elasticity equations are solved for cubic-to-tetragonal phase transformation in NiAl shape memory alloy. The effects of interfacial stress are studied for martensite-martensite interfaces in detail, which was absent in 1. Additionally, stress and temperature-induced growth of the martensitic phase inside austenite and twining are simulated. Some of the nontrivial experimentally observed microstructures reproduced in the simulations 1 are analyzed in detail. It includes tip splitting and bending, and twins crossing. This theory can be extended for electric, reconstructive, and magnetic phase transformations.