The TWO OF YOU should sit down with the doctor to talk about this.
If he won't, have him read this website to see how many of us there are are - me included - who've become pregnant after a vasectomy.
Or, print out the summaries of a couple of studies about pregnancy after vasectomy (search the web or ask you dr for the info) for him to read.
But, as others have said, if he doesn't believe you haven't cheated then you need to do some work on your relationship - especially if you're going to have a child together.
It's actually simple. DNA testing. Though if you've been faithful, and he doesn't believe you then you guys might want to sit down and talk about your relationship. The least he can do is give you the benefit of the doubt (because no procedure is 100% and everything does have a fail rate) You need trust in a relationship.
heyy, sorry to hear about whats going on.. have you seen paper work stating that his sperm count is at 0%? if so well mistakes happen the doctors could be wrong stuff happens.. not meaning to sound crazy but for instance i am pretty sure u have heard of or seen the show Maury well it has been a time when this guy have had a vasectomy, so anyway the couple had gotten a dna test and it proved he was the father so **** happens.. he should just wait it out until the baby comes to do a test since he does not believe u or maybe there could be some type of early testing.. try asking other doctors to get some different results. hope everything turns out well