We present a method for simultaneously measuring the thickness and the group refractive index of a specimen using self-referenced spectral-domain fiber-based interferometry. By removing the scanning part and using the fiber-based configuration, the system complexity and stability could be significantly improved. To minimize the system drift, we utilized the signals originated from the fiber ends of both arms. Implementing in a self-referenced configuration, we could improve the measurement accuracy down to a decimal place. Experimental measurements were made with a $1.555\mathrm{mm}$ thick fused silica plate. At $814\mathrm{nm}$ the thickness was measured as $1.5546\pm 0.0002\mathrm{mm}$ , and at the same time, the group index was obtained as $1.4627\pm 0.0002$ .