well my spouse if Lebanese but he was raised and lived all his live outside Lebanon. He doesn't always get my jokes, I don't always get his, we sometimes seem to be thinking about one thing differently but at the end of the day I think we are a perfect match.
I always say he took the best of being Lebanese and the best from the English Society ( best of both worlds as they say)
think the same about your kids, make sure you teach them Arabic, not only at home but also send them to Arabic school ( I am sure there should be one available where you are) make sure they read and write Arabic, it will not only be a cultural thing but a plus on their CV :P
my brother in law is married to non-Lebanese, he always tells his mum I'm gonna get you the kids to raise to make sure they will learn Arabic properly ( his mum was an Arabic Teacher in London ), however if you are saying you do not see your parents that often you might need to make sure that the language would not be lost and this has to be a personal effort.
My cousin is married to a Lebanese, they both live in the U.S. their kids were born and raised there ( I am sorry to say but now non of their kids ( 3 of them) can speak Arabic and non of them know anything about Lebanon, I'll have to say it is back to the parents, how often can you take them Lebanon? how long can you stay there?
So even if your husband is Lebanese, with you loving abroad that is a risk that your kids will only get part of what you got about this culture.
I was once told, we only took I do not maybe 50% of connections and knowledge of our culture of what our parents had ( since we did not live all our lives in Lebanon), our kids will take less than 50% from us, since they will be born and raised in the west and then do not even think about their kids.
It is sad but true, we are sacrificing certain things for us to have a better life ( well at least that what we convince ourselves)
So as said there is a lot of personal effort involved I am afraid but if it works it is definitely worth it