This paper reports results obtained from isothermal-isobaric molecular dynamics simulations of binary fluid mixtures composed of atoms and homonuclear diatomic molecules. Intermolecular interactions between atoms are represented by the one-center Lennard-Jones potential and those between diatoms are represented by the two-center Lennard-Jones potential. Simulations are performed over a range of molecular elongation 0 less than or equal to I-D = L/sigma(D) less than or equal to 0.8. Molecular size and energy parameters of the components are kept the same. Results are reported for density, internal energy, excess Gibbs free energy, excess enthalpy and excess volume of several equimolar mixtures at a temperature, k(B)T/epsilon(A) = 0.92, and pressure, P sigma(A)(3)/epsilon(A) = 0.5. Excess Gibbs free energy has been determined accurately using the reliable coupling parameter charging method. We show how thermodynamic properties respond to changes in molecular elongation. Also, we have used our simulation results to test a new version of the first-order perturbation theory of two-center Lennard-Jones fluid mixtures based on the nonspherical reference system. In this theory, correlation functions of the reference fluid mixture are approximated by those of the hard sphere mixture. It has been found that this version of the perturbation theory can describe density and internal energy up to l(D) = 0.8, and it can predict simulation results for excess properties accurately for l(D) < 0.6.