Learn English – the meaning of “nothing’s written in stone.”

In the absence of further context, I believe the definition of 'record' you are looking for is this one:

The sum of the past achievements or performance of a person, organization, or thing.

I believe that Hitchens is saying that Marvin Olasky is claiming that he has become a better husband since becoming a Christian. It is likely, as they are discussing religion (thus morality/ethics) in context to being a 'better husband', that he is refering to improved devotion/understanding/supportiveness/ faithfullness to his partner etc. So the sentence could be reworded as:

"He’s a convert from both Judaism and Communism. He tells the audience that since becoming a Christian he has become a better husband. I’m ready to believe it."

"It is two years since Paul and Jane moved to Paris." is still correct, even though less common.

For example, have a look at this quote by Sally Brampton (which is the best example Google spewed out at a quick glance — I'm sure there are many more to find)

It is two years since I emerged from depression and I no longer want myself dead.
I want myself alive.

You might also want to have a look at English Grammar in Use : a reference and practice book for intermediate students of English by Raymond Murphy.