Google Aspergers Spectrum Quotient test - it has fifty questions.
I am more than convinced that xH is on the spectrum - so much fits. When things got better between us in terms of communication last summer, I asked him if he had ever been assessed. He basically refused to accept that this was a possibility. He scored himself really low on the test, whereas I would have scored him high.
Obviously, it would be wrong for me to question his self-perception as he is the one who needs the strategies to function in life. But he basically even ignored the basis on which I raised the issue (wanting to try to understand and improve communication) and deflected it back to me.
This really left nowhere to go. If he had pursued a diagnosis, then it would have given us some tools to work with. Whereas he did not acknowledge his part, whatever that was, and was clear he couldn't change. I was not even asking him to change. I just wanted to have more of a map to understand. Otherwise it was all me with the problems and that is never a true reflection of a marital situation.
So to your situation, I think you are right, formal assessment - this gives you the information to try to understand the situation fully. It does not give you a solution, but otherwise you are acting and making decisions without knowing the issues.
If he is diagnosed, you can seek counseling with a therapist experienced in ASD marriages. If you separate, there are websites which talk about separation and divorce when one person is AS. I did not realise the latter when we separated, but to be honest, some of the horror stories reflect my own three year long experience so far. A diagnosis is information you need, regardless of outcome of your marriage.
There is also a website Different Together for people married to people with ASD. Again, had I read it earlier than I did, I might have known what I was dealing with sooner.
And if there is no formal diagnosis, then nothing has changed since before he suggested this could be a possibility. I would be curious to know why he thought to do the test now, though.
Nonetheless, until he seeks a diagnosis, it is a side show to the day to day issues. It is not an excuse for EA. It also does not mean you need to forget the EA aspects. But it is a side show worth keeping on your radar, because if he does seek assessment and is prepared to work on aspects of communication around this etc that is a good thing, regardless of the outcome of your marriage.