I assume you and your FWB are sexually involved, so when you go to see him, your husband knows that sex is happening.
Did you just start having sex with the FWB after telling your husband you are poly, or did you and your husband sit down and negotiate boundaries and how to proceed? Did you ask what hubby would be comfortable with and offer to take things slowly so he could get used to this change in the dynamic of your relationship? Start out with hand-holding and kisses before jumping into bed with the FWB, and talk with your husband about how it affects him each step of the way?
Six months is a fairly short time to go from announcing you are poly to overnights with a FWB. I wonder if the moodiness or difficulties he is having might be due to his feeling like his needs aren't being considered. Also, I don't know anything about your financial situation, but some guys, if they are the main breadwinner, develop resentment if they feel they are just paying for their wife to go on dates with someone else. Did you two address how you would pay for your expenses of going out with this guy, and anything related to it (lingerie, travel, presents, condoms, birth control, sex toys, etc.)?
Are you also making sure to have a date night with your husband every week so that he doesn't feel like he's stuck with just ordinary sharing the household responsibilities?