Under Austrian rule, between 1816 and 1866, parish priests were required to record births, marriages and deaths in their registers. Most, but not all, parish registers are now kept in the archives of the diocese they belong to which are open to the public. This is the website of the archives of Veneto's dioceses: https://siusa.archivi.beniculturali.it/cgi-bin/pagina.pl?RicProgetto=ev
Of course, that means you need to know in what city, town or village your ancestors lived, in order to fruitfully search the local parish registers.
If the family you're looking for lived in a province other than Venice, you're more likely to find something in the corresponding Archivio di stato (there is one for every province). If you don't know in what parish they lived you may find some clues in the notaries' acts. There are extensive, albeit not complete, lists of those who signed a notarial act sorted by family name. If you find an act, it usually shows the age, father's name and dwelling (residence) of the signers. These lists and the acts you can find in the Archivio di stato of the province where they were signed.