We have used magnetophotoluminescence measurements to establish that InP/GaAs quantum dots have a type-II (staggered) band alignment. The average excitonic Bohr radius and the binding energy are estimated to be 15 nm and 1.5 meV, respectively. When compared to bulk InP, the excitonic binding is weaker due to the repulsive (type-II) potential at the heterointerface. The measurements are extended to over almost 6 orders of magnitude of laser excitation powers and to magnetic fields of up to 50 T. It is shown that the excitation power can be used to tune the average hole occupancy of the quantum dots and hence the strength of the electron-hole binding. The diamagnetic shift coefficient is observed to drastically reduce as the quantum dot ensemble makes a gradual transition from a regime where the emission is from (hydrogenlike) two-particle excitonic states to a regime where emission from (heliumlike) four-particle biexcitonic states also becomes significant.