My husband is muktzeh (he was born in the eighth month and is now nineteen). Our marriage is going well. However, sometimes on the three-day Yom Tov it becomes difficult that neither I nor anyone else can p̶a̶s̶s̶ ̶h̶i̶m̶ ̶t̶h̶i̶n̶g̶s̶ pass him to things at the table. Is there any solution for this?
From RaMBa"M's Hilchot Milah - Chapter 1
Nevertheless, if such an infant remains alive for thirty days, he is considered to be a child who will live and is governed by all the same rules as other infants.
From this, I gather that since your husband is muktzeh, he must be younger than 30 days old (your question says he's 19, so I'm assuming you mean 19 days old). Since you are implying that you are not muktzeh you must be older than 30 days old, but I will assume that you are also somewhere close to this age range so that things aren't as creepy.
As it turns out, since your husband is so young, you can't really be married after all. While the kiddushin can happen at a very young age, the minimum age for a marriage to take effect is 13 for boys and 12 for girls. So simply don't worry about it. Go play with your mommy and daddy for a few more years and then you can safely marry your husband when he turns 13 without any concern for him being muktzeh.
As someone who was born on the 9th day of the eighth month of the seventh year (of this century) of the sixth millenium (9 Cheshvan, 5707) I can understand your problem. Even if your husband is muktzah you do not have a problem.
First, being muktzah just means that you would not be allowed to move him from one place to another. Thus, you would not be allowed to pick him up and pass him to someone else. You would be allowed to pass to him other items at the table or to put something down next to him so that he can pick it up.
Second, since the two of you are married, he is a Kli shemelachto l'heter. Thus it is mutar to move him letzoraech gufo or letzorech mekomo. You would also be allowed to move him letzorech mitzvah. Thus oneg shabbos or oneg yom tov would also be allowed. This allows any of the things that are part of the oneg including those actions that require you to move or touch him.