We present x-ray diffraction (XRD) investigations of the structure of nominally lattice-matched GaInAs/InP multiple quantum well (MQW) structures grown by chemical beam epitaxy (CBE). To obtain information about the individual MQW layers and the interface structure we make use of the x-ray interference effect between two layers of equal lattice constant but different layer thickness separated by ultrathin strained (interfacial) layers. This effect predicted by the dynamical diffraction theory provides a powerful tool to quantitatively investigate ultrathin single quantum well structures and monolayer thin interfaces as well as MQW structures. For a given switching sequence during CBE growth, we determine the interface structure of GaInAs/InP MQW structures within the limits given by XRD theory. Additionally we found that an As gradient from the GaInAs quantum well layers into the InP barrier layers is present. The influence of the substrate off-orientation, the growth rate, and the group V flux in the InP barriers on the total amount of strain incorporated into the InP layers is shown. The obtained results indicate that the mechanism of As incorporation into InP layers is similar to the mechanism observed for the As incorporation into (qua)ternary GaxIn1-xAsyP1-y layers.