The linear density response formalism is used to analytically obtain an effective pairwise interaction potential of charged particles that simultaneously takes into account quantum mechanical and quantum statistical effects in weakly and moderately non-ideal plasmas at thermal equilibrium. The static dielectric function is obtained by interpolating long -and short wavelength asymptotic forms of the dielectric function in the random-phase approximation. The exchange effects are neglected in the micropotential, while the quantum-statistical effects are accounted for in the screening. The effective potential constructed in such a way takes a finite value at the origin and proves to be screened at large distances. The thermodynamic properties of two-component plasmas are then calculated and comparison is made with some data available in the literature.