Several IP-based routing algorithms have been developed for low-Earth orbit (LEO) satellite networks in recent years. The performance of the satellite IP networks can be improved drastically if multiple satellite constellations are used in the architecture. A multilayered satellite IP network is introduced that consists of LEO, medium-Earth orbit (MEO) and geostationary Earth orbit (GEO) satellites. A new multilayered satellite routing (MLSR) algorithm is developed that calculates routing tables efficiently using the collected delay measurements. The performance of the multilayered satellite network and MLSR is evaluated through simulations and analysis.