We present a complete study of the diffuse ionized gas (DIG) in a sample of six spiral galaxies (NGC 157, NGC 3359, NGC 3631, NGC 6764, NGC 6951, NGC 7479) using very high quality Hα images which allow analysis down to very low surface brightness (between 0.3 and 2 pc cm-6). Separation of the diffuse Hα emission from that of the H II regions was performed using the most reliable method: subtracting from the integrated Hα flux of a complete galaxy the contribution from its fully catalogued population of H II regions. The integrated luminosity of the DIG is considerable ( ~ 1040-1042 erg s-1) and is a high fraction of the total Hα emission of each galaxy. Lower and upper limits to the DIG emission in Hα were derived. The lower limits vary from 25% to 50% and the upper limits from 45% to 70%, in our observed sample. Previous studies of a very small number of objects, showed that there is a spatial correlation between the DIG and the H II regions in spiral galaxies suggesting that the DIG is photoionized by Lyman continuum photons (Lyc) which leak from H II regions. Here we go further: we show that the correlation of the DIG is stronger with the most luminous H II regions and we propose a specific model for the ionization of the DIG: we show that the luminosity, in Lyc photons, leaking from the most luminous H II regions is enough to ionize the diffuse gas in a model where the H II regions with luminosities greater than LHα>= 1038.6 erg s-1 are density bounded (Beckman et al. cite{gordo}). This model predicts that a fraction of this flux escapes from the galaxy into the surrounding medium.