Yes yes and more yes.
Breastfeeding supressing ovulation and a woman's sex drive in inextricably linked to her fertility. You aren't fertile right now which is why you have no period and no sex drive. Our hormones encourage us to have sex when we are able to become pregnant! I read a study a few years ago that women are also more likely to choose sexy clothes, high heels and go out on the town when they are ovulating! Ha!
My youngest son is 13 months old and I am still breastfeeding him, though we are down to twice a day. I still haven't gotten my period back (haven't had it since 2008!!) but my desire has returned a little bit. Don't discount the fact that you are also tired and stressed from having three little ones to look after, that has a huge impact on sex drive too. I always found that my sex drive got better after the littlest one started sleeping through the night.
As far as how to deal with hubs, encourage him to read the responses you get so that he sees that it is not you. And also, I try to make sure that we do have sex regularly, even if it isn't always "good for both of us". My husband was prepared this time around although it was a major issue after our first son was born. We got through it and things got back to normal, then we had to go and wreck it and have another baby. Ha!
Good Luck! Like ever other baby phase, this too shall pass!