Here, we study the resonant photonic states of photonic double quantum well (PDQW) heterostructures composed of two different photonic crystals. The heterostructure is denoted as B/A/B/A/B, where photonic crystals A and B act as photonic wells and barriers, respectively. The resulting band structure causes photons to become confined within the wells, where they occupy discrete quantized states. We have obtained an expression for the transmission coefficient of the PDQW heterostructure using the transfer matrix method and have found that resonant states exist within the photonic wells. These resonant states occur in split pairs, due to a coupling between degenerate states shared by each of the photonic wells. It is observed that when the resonance energy lies at a bound photonic state and the two photonic quantum wells are far away from each other, resonant states appear in the transmission spectrum of the PDQW as single peaks. However, when the wells are brought closer together, coupling between bound photonic states causes an energy-splitting effect, and the transmitted states each have two peaks. Essentially, this means that the system can be switched between single and double transparent states. We have also observed that the total number of resonant states can be controlled by varying the width of the photonic wells, and the quality factor of transmitted peaks can be drastically improved by increasing the thickness of the outer photonic barriers. It is anticipated that the resonant states described here can be used to develop new types of photonic-switching devices, optical filters, and other optoelectronic devices.