We report a study of the interfaces of InGaAs/InGaAsP quantum wells (QWs) grown by gas-source molecular beam epitaxy. By optimizing the group-V source supply sequence, a photoluminescence (PL) linewidth as narrow as 6.6 meV has been observed from a 2 nm wide single QW. The PL linewidths have been analyzed to evaluate the contributions of alloy compositional scattering and interface roughness. The analysis shows that for QW structures grown with the optimized growth sequence, the PL linewidth is mainly due to alloy compositional variations, whereas the contribution from interface roughness is small, indicating a good interface control. By considering the strain effect on the band alignment of the InGaAs/InGaAsP heterojunction, theoretical transition energies of QWs have been calculated using the envelope-function approximation, and the results agree well with the experimental data.