This study deals with the vibration transmissibility of a vibration isolation device, which is composed of frictional damping and nonlinear softening springs, when its base is harmonically excited. The SCAP method, a type of averaging method, is employed to obtain steady-state responses. The vibration characteristics due to excitation of the base are investigated through the analysis of displacement transmissibility in the steady-state response. In this process, displacement transmissibility for design parameters is analyzed, and the stability of the response is also investigated. The vibration isolation effect due to frictional damping is found to be more effective in the case of the softening spring than in the case of the hardening spring. Additionally, the pattern of the jump phenomenon observed during frequency sweeping, both upward and downward, has been identified.