InGaAs/AlAsSb quantum well structures have been grown by molecular beam epitaxy nominally lattice matched to InP substrates and characterized by photoluminescence. The exciton transitions from the n=1 electron to heavy-hole subbands were investigated and the band-edge discontinuity of an InGaAs/AlAsSb heterostructure was evaluated using an envelope function method. The type I band lineup with a band-edge discontinuity was estimated to be about 1.6 eV for As terminated samples, which exhibit the lowest compositional fluctuations across heterointerfaces. The dominant photoluminescence line-broadening mechanisms were found to be monolayer fluctuations in the well width and a random alloy compositional variation in sublayers, as well as exciton-optical phonon scattering. Using an optimized growth condition, short intersubband transitions in the 1.3-1.5 mum wavelength range were measured in the coupled double quantum well structures.