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Long-slit spectrophotometry obtained simultaneously in the spectral ranges λλ3950-4900A and 8000-10500A is presented for a number of giant extragalactic HII regions (GEHRs) in the spiral galaxies NGC 628 and NGC 2403. These ranges include lines from the Balmer and Paschen series of hydrogen separated by a wide wavelength interval. The Paschen and Balmer lines with special emphasis on the corresponding multiplet lines Pδ/Hε are used to examine the dust extinction towards the GEHRs in these galaxies. We find good internal consistency for the observed/predicted line ratios used for derivation of the visual extinction, A_V. Our results for A_V are in general larger than previously published values based on the Hα/ Hβ ratio with the GEHRs in NGC 628 exhibiting the largest extinction.