A heterodyne metrology interferometer was stabilized down to a noise level of 20 picometers (pm) as a root-mean-square (RMS) value integrated between 0.3 mHz and 1 Hz. This noise level was achieved by employing active and passive interferometer stabilization techniques. The heterodyne interferometer was built on a 50 mm square ultralow expansion glass plate in order to reduce an optical path length change caused by temperature variation. An optical configuration of the interferometer is a Mach-Zehnder interferometer with a design as symmetric as possible so that a detection signal can be insensitive to homogeneous thermal expansion of the glass plate. The heterodyne frequency is actively controlled in order to suppress residual noises caused by optical path length changes outside of the glass plate as well as phase fluctuations of the heterodyne frequency source. Our stabilization scheme is considered useful in achieving the 20 pm noise level without a stable heterodyne frequency source, as well as temperature stabilization around a whole apparatus. This interferometer can be used in precise metrology applications, such as characterization of deformation for satellite optical components against thermal exposure.