Picosecond acoustic interferometry was used to study the acousto-optic properties of a distributed Bragg reflector (DBR) manufactured from two immiscible polymers (cellulose acetate and polyvinylcarbyzole). Picosecond strain pulses were injected into the structure and changes in its reflectance were monitored as a function of time. The reflectance exhibited single-frequency harmonic oscillations as the strain pulse traversed the DBR. A transfer matrix method was used to model the reflectance of the DBR in response to interface modulation and photo-elastic effects. This work shows that photo-elastic effects can account for the acousto-optic response of DBRs with acoustically matched layers.