I've been to Japan twice and it is indeed a wonderful trip. Once was on my own as an exchange student and the other trip was with my husband as a vacation (before we had our daughter).
I would ask him to work with you on this since you very much want to go. Have you told him, in just the way you tell us here, that you are longing to see Japan and you want to make memories there with him? Or is he just assuming that because of work you can't do it so he's forging on with his own plans, unaware of how much you reallly want to go? If you are holding back on telling him your feelings because you want to spare him somehow -- don't. He needs to know that you are sad and envious. This is important: He should be able to take that news like an adult and see that it means you want to be with him there -- not out of some lack of trust but out of an abundance of love both of him and of adventure. So TALK to him and don't be skittish about telling him that you want to go too and as a couple you want to work it out so you both have the trip of a lifetime. Think about him showing you photo after photo of a place you want to see and you sitting there either sad or steaming or regretful because you missed it.
Since he has a friend there who can provide lodging -- can that friend provide lodging for you both? Can your husband wait to go when you can get off work and both of you would go take advantage of this free lodging? Or is this friend's lodging either (a) available only at some specific time when you can't go, or (b) so tiny that it can only accommodate your husband? (I find the latter hard to swallow!)
I would talk to him about either your going together or possibly saving up to go at a time when you are both able to make it. Look into packages and staying in traditional Japanese inns that are cheaper than large city hotels (some inns are very pricey but others are very reasonable). Really you and he need to work this out as a trip for you both. If you don't have kids now, you will discover that once you do have kids, this trip will then be postponed for many years. Find out what you can change or sacrifice to go, but don't let him and the "free lodging" deal drive everything -- it would be better to give up the free lodging and wait and plan a great trip TOGETHER in, say a year's time, than for him to insist on going alone solely because he gets free digs.