A series of (Ga,In)As/GaAs/Ga(As,Sb) multi-quantum well heterostructures is analyzed using temperatureand power-dependent photoluminescence (PL) spectroscopy. Pronounced PL variations with sample temperature are observed and analyzed using microscopic many-body theory and band structure calculations based on the k·p method. This theory-experiment comparison reveals an unusual, temperature dependent variation of the band alignment between the (Ga,In)As and Ga(As,Sb) quantum wells.