InAsP/InP strained multiple quantum wells (MQWs) with specular surfaces were grown on InP (111)B substrates by gas-source molecular beam epitaxy. Cross-sectional transmission electron microscopy and high-resolution x-ray rocking curves show that the InAsP/InP (111)B MQW structures possess sharp and uniform interfaces, excellent periodicity, and crystalline quality. Structural parameters were extracted accurately from a dynamical-theory simulation by considering the anisotropy of the (111) strain tensor. Low-temperature photoluminescence and photoluminescence excitation measurements revealed interband excitonic transitions, and the energies agree with a calculation with an internal piezoelectric field taken into account.