The configurational entropy of interacting linear molecules (k-mers) absorbed on a regular lattice is addressed through analytical as well as numerical methods. The general definitions for computational exact calculations of k-mers lattice-gas entropy are presented. In addition, theoretical basis for accurate analytical estimations of the entropy of reference states are given. The coverage and temperature dependence of the configurational entropy of interacting adsorbed dimers on one and two-dimensional lattices are obtained. A novel phase behavior of k-mers lattice-gas is shown and discussed.