The magnetohydrodynamic (MHD) normal modes of oscillation of sheared coronal arcades including longitudinal wave propagation are studied. Solutions have been computed in order to ascertain the effects of the longitudinal magnetic field component, By, and of the longitudinal propagation, ky in these structures. Our results show that whenever By = 0 and/or ky = 0 fast modes, characterized by a global velocity structure and a discrete spectrum of frequencies, and Alfvén continuum modes, characterized by a velocity perturbation confined to given magnetic surfaces, get coupled and no pure fast modes nor pure Alfvén modes exist, but modes with mixed properties arise. These oscillatory modes display a global spatial distribution together with a non-square integrable singular behaviour on certain magnetic surfaces. Under certain circumstances, moreover, this mode coupling is such that the Alfvénic contribution is also in the form of a smooth velocity profile covering a range of magnetic surfaces instead of a singularity on a fixed magnetic surface. The coupling between fast and Alfvén modes is governed by the parity of their eigenfunctions in the direction along the equilibrium magnetic field. The "parity rules" determining the features of coupled modes in terms of their parity, ky and By are presented.