You cannot have both an FSA and an HSA at the same time. Since your FSA is with your own employer, they will definitely let you continue contributing to it because they don't know about the HSA with your husband's plan. BUT you will pay for it at tax time since the IRS does not allow it.
This was a HUGE problem at my old employer. My husband has an HSA, but one of our benefits was to get $90 a month into FSA. I legally could not have an FSA (you can have a limited FSA for dental and vision only, but they didn't offer that). Every year it was a huge fight for them to take me off this benefit,
and then I had to watch my paychecks because mid-year someone would always "fix" the omission and I'd have an FSA again!