In this paper three-phase fiber-reinforced matrix is analyzed using analytical micromechanical model named simplified unit cell method (SUCM). The system consists of transversely isotropic elastic nanotube and viscoelastic matrix and interphase region. This interphase region comprises considerable volume fraction of the system because of large surface area per unit volume of the nanotubes. However, volume fraction of the interphase in particular short fiber system is considerably small to contribute to the whole properties of it. The presented closed-form solutions are able to predict the effective response of the three-phase fiber-reinforced matrix in any combination of normal and shear loading conditions. To verify the results, creep compliance of Graphite/Epoxy in $10^{circ}$ and $45^{circ}$ and $90^{circ}$ off-axis conditions are compared with existing data. Nanotube/Polycarbonate is also examined to investigate the effect of interphase on viscoelastic behaviors of nanocomposites.