I wanted to express my sympathies after reading your heatbreaking post.
It certainly sounds like there is more going on with your husband.
Regardless of diagnosis, the moment a couple decides to have a family and they encounter problems, then it really is a joint issue. There is no blame in the context of infertility, just an explanation (diagnosis) or description. Oftentimes people who are not struggling with infertility want to point the finger at someone for the struggle. That all changes when you are part of the struggling couple.
Truth be told the diagnosis is Male Factor. Infertility is emaculating to begin with and when that is the diagnosis I am sure it only compounds the issue. (one of my husband's "friends" used to tease him in a crude manner. I overheard him once and almost went feral. I was never a fan of that person and that pretty much terminated the friendship.)
Your husband is unfairly scapegoating you. He elected you to make the call about when to proceed with the family-building. That is a decision. If he wanted to start earlier. If he really, really wanted to start a family with you earlier he would have made that clear. He chose not to. To ignore the male factor and focus on your age is not fair to either of you, actually because infertility is something that both of you need to face as a united front. (although male ambivalence and foot-dragging is very common. My husband is the poster-boy.
Yes you are 38 but it does not mean all hope is lost. It just means the context of your treatment will be different from that of a woman in her early 30s or 20s. I also think that Dr. H is quick to recommend donor eggs to women in your age group.
Unless... Did you tell your husband that you are younger than you actually are?
(trying to lighten the mood)
I have faced struggles on this road. It is not easy but keep breathing and hold your head high. Maybe during your next appointment Dr. H can speak to the male factor issues more frankly. Men often defer to other men and so much of this process is focussed on the woman & the men feel left out. (and emasculated) Being a man, Dr. H may be able to garner some of your husband's trust in a way that will help him see things differently and in their full and proper context.
And I cannot say enough good things about meeting with a counsellor who specialises in infertility. Even though your husband is not "there" yet, it can certainly help you navigate some of these choppy waters and give you the tools to have a dialogue with your husband in a meaningful way that takes blame out of the equation.
Wishing you the best. We are here for you.