Hi K.,
First off, let me say how much I admire your ability to see the very necessary contributions your husband is making at this time. Even if they are not financial, they are extremely valuable to all of you.
As a nanny, and as a friend, I have witnessed several families go through hard transition times such as the one you are describing. Let me put your mind at ease by saying that a husband being out of work is a stress on the very best of relationships. Men often find their identity and self-worth in being "the breadwinner". Conversely, in our culture, many people often associate a husband who is between jobs as being less masculine or even dependent. Perhaps your husband is feeling this. I know that the tension between the couples that I was privy to was palpable at times. So please, know that what you and your husband are experiencing is very "normal".
That said, what I have heard in retrospect from most of these women was that things were worsened when they tried to help their husbands look for work. I know it seems perverse, but I am guessing that for the guys, it must feel like "She doesn't even think I'm capable of getting a job by myself." We women see it as helping (we are wired that way, to network and solve our problems socially-- men aren't), but men often don't appreciate it at all, and may even feel like we consider them to be less capable. And, in truth, when we enter the bedroom as a couple, we both want to come together as equals. "Helping" our husbands when they don't specifically ask for our help can really put a huge damper on our intimate lives with them.
Here's one more thing to add: your husband may also be experiencing some feelings of conflict similar to what many women experience. When we have a chance to stay at home with our children, many of us will feel compelled to look for work (for so many very worthwhile reasons--to contribute financially, to cultivate a life outside the home, for the love of the work that we do), but feel very torn. We relish those moments of just being present with our children and all of the little discoveries that happen within them, and at the same time, we know that this may not be all that we need to be fulfilled. It can be incredibly emotional transition for any parent, and I think it's important to acknowledge that some men feel this just as keenly, but aren't really encouraged to discuss it. Add that to all those other feelings and there's a lot to not talk about if you are a traditional sort of guy.:)
I loved your letter. If it were me, I would rewrite it for him, focusing solely on what a great parent and partner he has been while he's been at home. Let him know how much you appreciate his help and his being there. Let him know how much you respect how hard he's working for all of you. Let him know that you will respect his course of job-hunting and will let him lead; that you'll be happy to help if he asks you to directly, but that he probably would be happier taking this on on his own. Let him know that you miss the intimacy, that you don't place blame, and how much he means to you, just for the person he is.
You have an incredible love for your husband, and if you give him some time and your patience, you will get through this. It takes a while to shake out, from what I've seen, but things will get "back to normal".
My best to you.