Motor proteins are active enzyme molecules that play a crucial role in many biological processes. They transform chemical energy into mechanical work and move unidirectionally along rigid cytoskeleton filaments. Single-molecule experiments indicate that motor proteins, consisting of two motor domains, move in a hand-over-hand mechanism where each subunit changes between trailing and leading positions in alternating steps, and it is assumed that these subunits do not interact with each other. However, recent experiments on heterodimeric kinesins suggest that the motion of motor domains is not independent, but rather strongly coupled and coordinated, although the mechanism of these interactions is not known. We propose a simple discrete stochastic model to describe the dynamics of homodimeric and heterodimeric two-headed motor proteins. It is argued that interactions between motor domains modify original free energy landscapes for each motor subunit, while motor proteins still move via the hand-over-hand mechanism but with different transition rates specified by the new free energy profiles. Our calculations of biophysical properties agree with experimental observations. Several ways to test the theoretical model are proposed.