The LISA Technology Package (LTP) uses laser interferometry to measure the changes in relative displacement between two inertial test masses. The goals of the mission require a displacement measuring precision of 10 pm Hz^−1/2 at frequencies in the 3–30 mHz band. We report on progress with a prototype LTP interferometer optical bench in which fused silica mirrors and beamsplitters are fixed to a ZERODUR® substrate using hydroxide catalysis bonding to form a rigid interferometer. The couplings to displacement noise of this interferometer of two expected noise sources—laser frequency noise and ambient temperature fluctuations—have been investigated, and an additional, unexpected, noise source has been identified. The additional noise is due to small amounts of signal at the heterodyne frequency arriving at the photodiode preamplifiers with a phase that quasistatically changes with respect to the optical signal. The phase shift is caused by differential changes in the external optical paths the beams travel before they reach the rigid interferometer. Two different external path length stabilization systems have been demonstrated and these allowed the performance of the overall system to meet the LTP displacement noise requirement.