Qubits based on the singlet (S) and the triplet (T(0), T(+)) states in double quantum dots have been demonstrated in separate experiments. It has been recently proposed theoretically that under certain conditions a quantum interference could occur from the interplay between these two qubit species. Here we report experiments and modeling that confirm these theoretical predictions and identify the conditions under which this interference occurs. Density matrix calculations show that the interference pattern manifests primarily via the occupation of the common singlet state. The S/T(0) qubit is found to have a much longer coherence time as compared to the S/T(+) qubit.