The single-degenerate scenario for Type Ia supernovae should yield metal-rich ejecta that enclose some stripped material from the non-degenerate H-rich companion star. We present a large grid of non-local thermodynamic equilibrium steady-state radiative transfer calculations for such hybrid ejecta and provide analytical fits for the H alpha luminosity and equivalent width. Our set of models covers a range of masses for Ni-56 and the ejecta, for the stripped material (M-st), and post-explosion epochs from 100 to 300 d. The brightness contrast between stripped material and metal-rich ejecta challenges the detection of HI and HeI lines prior to similar to 100 d. Intrinsic and extrinsic optical depth effects also influence the radiation emanating from the stripped material. This inner denser region is marginally thick in the continuum and optically thick in all Balmer lines. The overlying metal-rich ejecta blanket the inner regions, completely below about 5000 angstrom, and more sparsely at longer wavelengths. As a consequence, H beta should not be observed for all values of M-st up to at least 300 days, while H alpha should be observed after similar to 100 d for all M-st >= 0.01 M-circle dot. Observational non-detections capable of limiting the H alpha equivalent width to <1 angstrom set a formal upper limit of M-st < 0.001M(circle dot). This contrasts with the case of circumstellar-material (CSM) interaction, not subject to external blanketing, which should produce H alpha and H beta lines with a strength dependent primarily on CSM density. We confirm previous analyses that suggest low values of order 0.001 M-circle dot for M-st to explain the observations of the two Type Ia supernovae with nebular-phase H alpha detection, in conflict with the much greater stripped mass predicted by hydrodynamical simulations for the single-degenerate scenario. A more likely solution is the double-degenerate scenario, together with CSM interaction, or enclosed material from a tertiary star in a triple system or from a giant planet.