We have investigated the properties of strain-compensated InGaAsP/InGaP superlattices, grown by metalorganic vapor phase epitaxy, with and without InP interlayers inserted in the InGaP barrier. Using cross-sectional scanning tunneling microscopy and spectroscopy, we observe lateral variations in layer thickness and electronic properties. When the number of superlattice periods is increased from 8 to 16, the growth front develops large undulations in the top two to four superlattice periods. For structures with InP layers inserted in the InGaP barrier, only slight undulations of the top superlattice periods occur. We discuss the origins of the growth front undulations in terms of the elastic relaxation of strain arising from thickness and/or composition variations in the superlattice layers. Finally, we observe a fourfold periodicity of the [001] atomic spacing, presumably arising from atomic ordering in the alloys.