Calculations of the photoionization cross section of the 2p and 3s subshells of free Ar and Ar@C-60 as examples have been performed using the molecular structure of the confined system and time-dependent density functional theory for the dynamical quantities. The results for Ar 2p in the combined system exhibit significant confinement resonances with the lower-energy ones being quite sharp, in contrast to the results of jellium-model calculations. In addition, calculations done with and without interchannel coupling between the photoionization channels of the 2p subshell of the Ar atom and the 1s subshell of the C-60 shell show that, in this case, the coupling is of negligible importance, even though the C 1s cross section is more than an order of magnitude larger than that of Ar 2p in the 300 eV range. The Ar 3s, which is not hybridized, also exhibits confinement resonances, but is very strongly affected by interchannel coupling with photoionization channels from the C-60 shell. The phenomenology of both 2p and 3s subshells is explained in terms of the interchannel-coupling matrix elements. These results should be applicable to inner-shell ionization of essentially any endohedral fullerene system