Idk how to make him believe me?

I have a situation i need to talk about. I dont want hubbs to know im going talk about this. He wanted me to keep it to myself. Not my friends or family.

Every so often i hang out with my coworker. Matter of fact. This was our 5th night out. Shes pretty funny and just really fun to hang out. I havent introduce her to my friend group.

One night my hubbs sister called and want to hang out. I was down to bring my co worker and my SIL together.

We hung out at a family bar. We took few photos all together. We didnt stay out that late. Since coworker and i had to be back to work the next day.

Next day i wake up and do my routine of swipping through FB and i seen my SIL posted "some" of photos. All of her and my SIL. I wish i snapped a photo of it. She had it say " 🤗out with my bff😜"

No photos of me, just them. While i was getting ready for work, i brought it up to the hubby. He said something on lines "maybe they hit it off and your little jealous". So i get to work.

I didnt see my coworker, until lunch. She met me at taco bell. The first thing she brings up is "Hate to sound rude, but your SIL was kind of weird."

I didnt bring up about the FB post. After somethings she felt uncomfortable about. Later that night i talked to my husband about what my coworker said. He got super mad. Thinking im throwing his sister underbus and this and that. He doesnt believe me about what my coworker said. Idk what to do?