We have developed a method to equip homodyne interferometers with the capability to operate with constant high sensitivity over many fringes for continuous real-time tracking. The method can be considered as an extension of the "J_1...J_4" methods, and its enhancement to deliver very sensitive angular measurements through Differential Wavefront Sensing is straightforward. Beam generation requires a sinusoidal phase modulation of several radians in one interferometer arm. On a stable optical bench, we have demonstrated a long-term sensitivity over thousands of seconds of 0.1 mrad/sqrt[Hz] that correspond to 20 pm/sqrt[Hz] in length, and 10 nrad/sqrt[Hz] in angle at millihertz frequencies.