I am going to recommend the Passionate Marriage book (with acknowledgments to oldtimer) and to suggest that MC combined with sexual therapy, as called for in the book, might be a good idea.
On the apparent low-desire of your H, I can relate to some of his anxiety, but on a level that I'm not too sure is typical or applicable. During the last year before our S, I was lower in desire than my now xW. I truly loved my W but because of the stress from work and the long hours, I was often too exhausted at the end of the day. I had the desire but it was so overridden by daily stress, that we never seemed to get together. We both seemed too busy and that got to be a bad habit. But more importantly, I was subconsciously feeling more and more alienated and I couldn't figure out why. I now know why, but not then -- I still trusted my W completely and assumed the depression I felt stemmed entirely from me. xW now claims I was LD throughout our enire M, but that is history revision by her. I think it began some time before S4 was born and began to grow steadily from then on. She began to put more and more pressure on me, making demands of me domestically, financially and maritally. In all avenues I felt like I was not measuring up to her demands. She placed demands that I was was not bringing in enough income, but at the same time complaining that I never helped out with the children or the house-hold duties (all not true) and then if I did not initiate sex with her by her schedule, I was SOL.
My blind, stupid reaction was to passive-aggressively respond by "not going where I was not wanted", if you know what I mean. In the back of my mind I was feeling like there was nothing I could do right by her, so it didn't matter. Our SL suffered greatly because we were hardly ever available for each other. And on those rare occasion we did ML, while I brought as much passion and animated rejoicing to our rendezvous (given the rarity of such occasions), she on the other hand seemed more and more distant and lifeless. She brought about as much ardor to our bed as a corpse -- I don't know what disturbed me more: mechanically performing with what I knew to be feigned passion or just lying there like a dead fish. (I apologize for the harsh characterizations, but that's the best way to describe it. If I look back at the woman I was married to up until about 2002 and compare her to the person thereafter, I would say they were two entirely different human beings.) I didn't just want sex, I wanted her -- all of her, mind body and soul -- and that was what I was not getting.
Is it any wonder why I was so deeply depressed and felt ML was pointless? But this is a fault of mine that I need to work on: if I feel there's no gain to some action, I tend to not do anything but wait and see if things improve before acting -- this obviously destroyed my M.
It's really hard for me now, in retrospect, to say just which of the two of us was really lower of desire than the other. For a long time after the bomb I took the blame fully. And xW used to shriek at me, post-bomb, that she couldn't believe how I could contain myself so well sexually around her (translation: she couldn't understand how I could not give into her demands since she withheld the "rewards" of our union so effectively.) She remarked that she thought I would make "a great monk". (My thought, without voicing it, was that I don't want to be a monk, I just want the passionate woman I married back, not this shrill unsatisfiable person.)
I guess what I am saying, Didi, is that in my case I was far from being low-desire, but I did contain my desires because I believed I had no real outlet for them, especially with my W. I felt stressed by everything in my life (not the least of which was xW) and that only promoted my further withdrawal and pulling back. I got tired of trying to meet her more than half-way and just gave up; I hunkered down, and hoped the storms would end. She took that as total rejection of her. I still loved her very much, but she chose to not see it.
What I didn't realize is that for her, sex=love, or more precisely, that sex is the measure she uses to sole gauge for whether a man loves a woman or not. Immature of her, I know, but it's something I never really understood about her until it was too late.
And yet she made the obstacles so difficult, raised the bar so high, that she made the task near impossible for me to achieve. It's as if she wanted us to fail (and that's something my IC had said). She shut me down. Either way, I still wonder, if there hadn't been this OM, would we have been able to turn things around.
Again, perhaps some form of C would help, Didi. And please read the book and see the line of thinking it offers.