Far-infrared magnetotransmission investigations have revealed coupling effects on hydrogenic impurity states in doped GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As coupled double quantum wells. Impurity transitions of the well-center donors were measured in several samples with identical well widths but different narrow barrier widths. Results agree with variational calculations for all samples when intersubband mixing and the difference in the masses in the well and barrier are taken into account. Evidence for intersubband mixing in double wells is also provided.